2-norm 2-norm A/D conversion abs function ac2poly function ac2rc function addstages method aliasing impulse invariance preventing reducing sinc functions all-pole filters See also IIR filters all-zero filters See also FIR filters AM See also amplitude modulation amdsb function amplitude demodulation amplitude modulation analog filters bandpass bandstop Bessel Bessel comparison Bessel lowpass bilinear transformation Butterworth Butterworth comparison Butterworth lowpass Butterworth order estimation Chebyshev Type I Chebyshev Type I comparison Chebyshev Type I lowpass Chebyshev Type I order estimation Chebyshev Type II Chebyshev Type II comparison Chebyshev Type II order estimation converting to digital design discretization elliptic elliptic order estimation frequency response frequency response example highpass impulse invariance inverse lowpass models plotting See also IIR filters analog frequency analog signals See also signals analysis parameters analytic signals angle function anti-symmetric filters AR filter stability AR models See also autoregressive (AR) models arburg function arcov function ARMA filters coefficients Prony's method Steiglitz-McBride method See also IIR filters armcov function ARX models aryule function ASCII files importing autocorrelation convert from LP coefficients convert from reflection coefficients convert to LP coefficients convert to reflection coefficients estimation multiple channel filters two-dimensional variance autocovariance multiple channels autoregressive (AR) models Burg method coefficients covariance method modified covariance method power spectral density (Burg method) power spectral density (covariance method) power spectral density (modified covariance method) power spectral density (Yule-Walker method) Yule-Walker method See also IIR filters autoregressive moving-average (ARMA) filters See also ARMA filters avgpower method band edges prewarping bandpass filters Butterworth Chebyshev Type I Chebyshev Type I example Chebyshev Type II design elliptic FIR FIR example impulse invariance transform from lowpass bandstop filters Butterworth Chebyshev Type I Chebyshev Type II elliptic FIR transform from lowpass bandwidth barthannwin Bartlett Hann window function comparison bartlett window function comparison Bessel filters characteristics limitations lowpass prototype besselap function besself function bias linear prediction power spectral density variance trade-off Welch bilinear function bilinear transformations characteristics output prewarping prewarping example bit reversal bitrevorder function blackman window function comparison blackmanharris window function comparison Nuttall block method bohmanwin window function comparison boxcar windows See also rectangular windows brackets buffer function Burg method characteristics example spectral estimation Welch's method comparison Burg spectrum object buttap function butter function Butterworth filters characteristics comparison generalized limitations lowpass order estimation buttord function C header files canonical forms naming conventions carrier frequencies cascade method cascades Cauer filters See also elliptic filters cceps function cell2sos function center frequency centerdc method cepstrum inverse function cfirpm function cheb1ap function cheb1ord function cheb2ap function cheb2ord function chebwin Chebyshev window function comparison cheby1 function cheby2 function Chebyshev error minimization Chebyshev Type I filters characteristics example lowpass order estimation Chebyshev Type II filters characteristics limitations order estimation chirp function chirp signals chirp z-transforms characteristics CIC filters exporting from FDATool to Simulink coding PCM coefficients accessing filter convert autocorrelation to filter convert filter to autocorrelation convert filter to reflection convert reflection to autocorrelation convert reflection to filter filter lattice linear prediction reflection coefficients method coherence definition linearly dependent data colors sptool GUI communications applications modeling simulation See also modulation, demodulation, voltage controlled oscillation compaction discrete cosine transform complex envelope See also Hilbert transforms context-sensitive help continuous signals See also signals continuous-time filters See also analog filters conv function conv2 function conversions autocorrelation to filter coefficients autocorrelation to reflection coefficients errors filter coefficients to autocorrelation filter coefficients to reflection coefficients functions (table) reflection coefficients to autocorrelation reflection coefficients to filter coefficients second-order section to zero-pole-gain second-order sections to state-space second-order sections to transfer functions state-space to second-order sections state-space to zero-pole-gain transfer functions to lattice transfer functions to second-order sections transfer functions to state-space zero-pole-gain to second-order sections zero-pole-gain to state-space convert method convmtx function convolution cross-correlation filtering matrix matrix function (convmtx) corrcoef function correlation bias cross-correlation linear prediction matrices See also autocorrelation, cross-correlation correlation matrices corrmtx function cosine windows cov function covariance definition methods modified covariance spectrum object spectrum object See also autocovariance, cross-covariance, modified covariance method cplxpair function cpsd function cross power spectral density definition cross spectral density definition See also power spectral density, spectral estimation cross-correlation discussion two-dimensional cross-covariance comparison to cross-correlation multiple channels czt function See also chirp z-transforms data markers multichannel matrix multichannel signals time vectors vectors DC component suppression dct function de la Valle-Poussin windows See also Parzen windows decimate decode deconv function deconvolution default session sptool GUI delays group noninteger phase signals demod demod function demodulation example dfilt function cascade convert structures copying direct-form antisymmetric FIR direct-form FIR transposed direct-form I direct-form I sos direct-form I transposed direct-form I transposed sos direct-form II direct-form II sos direct-form II transposed direct-form II transposed sos direct-form IIR direct-form symmetric FIR FFT FIR filter implementation lattice allpass lattice ARMA lattice autoregressive lattice moving-average maximum lattice moving-average minimum methods parallel scalar state space structures structures dfilt.cascade function dfilt.df1 function dfilt.df1sos function dfilt.df1t function dfilt.df1tsos function dfilt.df2 function dfilt.df2sos function dfilt.df2t function dfilt.df2tsos function dfilt.dfasymfir function dfilt.dffir function dfilt.dffirt function dfilt.dfsymfir function dfilt.fftfir function dfilt.latticeallpass function dfilt.latticear function dfilt.latticearma function dfilt.latticemamax function dfilt.latticemamin function dfilt.parallel function dfilt.scalar function dfilt.statespace function dft See also discrete Fourier transforms dftmtx function difference equations differentiators definition least square linear-phase FIR Parks-McClellan FIR digit reversal digital audio tape standards digital filters anti-causal Butterworth Butterworth order estimation cascade Chebyshev Type I order estimation Chebyshev Type II Chebyshev Type II order estimation coefficients comparison to IIR convolution convolution matrices design elliptic elliptic order estimation equiripple FIR order estimation FFT FIR overlap-add FIR design fixed-point implementation frequency response group delay description group delay function identification from frequency data IIR design implementation with filter impulse response impulse response definition initial conditions lattice/ladder structures models order phase delay definition poles second-order sections specifications state-space time-domain representation transfer functions representation transients transposed direct-form II structures types zero-phase zero-phase implementation zero-pole analysis zeros See also FIR filters, IIR filters digital frequency digitrevorder function diric function Dirichlet functions definition discrete cosine transforms definition energy compaction property example inverse reconstruct signals discrete Fourier transforms algorithms definition eigenvector equivalent goertzel IIR filter implementation inverse two-dimensional magnitude matrix phase power spectrum estimation signal length dependencies spectral analysis time-dependent two-dimensional See also fast Fourier transforms discrete prolate spheroidal sequences See also dpss discretization bilinear transformations filters impulse invariance downsample function dpss function example dpssclear function dpssdir function dpssload function dpsssave function dspdata object mean-square spectrum psd pseudospectrum dspdata.msspectrumd function dspdata.psd function dspdata.pseudospectrum function dspopts object duty cycles echo detection edge effects eigenanalysis eigenvector method definition root MUSIC spectral estimation spectrum object See also multiple signal classification method ellip function ellipap function ellipord function elliptic filters definition limitations order estimation encoding eqtflength function equiripple Chebyshev Type I filters Chebyshev Type II filters Chebyshev windows elliptic filters elliptic filters (analog) elliptic filters (Cauer) Parks-McClellan design error minimization weighted frequency bands estimation covariance method cross spectral density modified covariance method Yule-Walker method See also parametric modeling export filter window fast Fourier transforms example frequency response Goertzel algorithm implementation output fcfwrite method FDATool exporting to Simulink fdatool GUI analysis buttons computing coefficients design methods exporting filters filter architecture filter design specification filter implementation filter order specification filters structure frequency response specification group delay importing impulse response magnitude response M-files opening phase delay phase response pole-zero plots response type saving coefficients second analysis sessions step response FFT See also fast Fourier transforms fftcoeffs method fftfilt function fftshift function Filter block filter design sptool Filter Designer GUI See also fdatool GUI Filter Designer GUI See also fdatool GUI filter function description filter method Filter Viewer introduction open printing Filter Visualization Tool See also fvtool GUI filternorm function filters analog analog lowpass analog lowpass prototype anti-causal anti-symmetric bit reversal Butterworth Butterworth (generalized) Butterworth order C header file Chebyshev Type I Chebyshev Type I lowpass prototype Chebyshev Type I order Chebyshev Type II Chebyshev Type II order coefficients coefficients coefficients in sptool GUI convert coefficients to autocorrelation convert from reflection coefficients convert to reflection coefficients convolution design design digit reversal discretization elliptic elliptic order equiripple export filter and filtfilt functions comparison filter function filtstates object filtstates object FIR FIR design FIR single band frequency data frequency domain frequency transformations fvtool GUI implementation importing to sptool GUI initial conditions using dfilt initial conditions using filter function initial conditions using filtic function inverse analog inverse discrete-time lattice/ladder linear phase linear prediction linear system models linear time-invariant digital median filtering median function minimax minimum phase norm numerator and denominator length objects order overlap-add using dfilt.fftfir overlap-add using fftfilt phase delay phase distortion removal phase modulation phase response pole-zero editor renaming 694 sampling frequency sampling frequency saving Savitzky-Golay Savitzky-Golay design Schur realizations second-order sections second-order sections filtering second-order sections IIR specfications sptool GUI Filter Designer states step response structures types viewing zero-phase zero-phase implementation zero-phase response See also fdatool GUI, FIR filters, IIR filters, digital filters, analog filters filtfilt function filter function comparison filtic function filtstates object filtstates object FIR filters arbitrary response complex response constrained least square differentiators equiripple example frequency domain frequency response Hilbert transformers IIR filter comparison implementation interpolation Kaiser windows lattice/ladder least square and equiripple comparison least square linear phase least square multiband least square weighted linear phase linear phase Parks-McClellan multiband multiband example nonlinear phase response order estimation overlap-add Parks-McClellan method reduced delay response resample sptool GUI Filter Designer standard band types window-based windowing method fir1 function example fir2 function fircls function fircls1 function firls function differentiators firpm comparison weight vectors firpm function differentiators example filter characteristics firls comparison Hilbert transformers order estimation weight vectors firpmord function example firrcos function firtype method flattopwin flat top window function FM See also frequency modulation fopen function Fourier transforms See also discrete Fourier transforms, fast Fourier transforms fread function freqs function frequency analog angular center cutoff demodulation digital estimation modulation normalization Nyquist Nyquist prewarping spectrogram vectors frequency domain duality with time-domain filters FIR filtering lowpass to bandpass transformation lowpass to bandstop transformation lowpass to highpass transformation transformation functions frequency domain based modeling See also parametric modeling frequency modulation frequency response Bessel filters Butterworth filters Chebyshev Type I filters Chebyshev Type II filters elliptic filters error minimization evaluating example inverse Kaiser window linear phase magnitude monotonic multiband phase plotting sampling frequency freqz function sampling frequencies freqz method From Disk radio button FVTool SOS view settings fvtool GUI gauspuls function pulse trains gaussfir Gaussian monopulse Gauss-Newton method analog domain discrete domain gausswin Gaussian window function generalized Butterworth filters generalized cosine windows generalized filters generate method Gibbs effect reduced by window gmonopuls function GMSK goertzel function graphical user interface (GUI) See also sptool GUI, fdatool GUI, wintool GUI, fvtool GUI, wvtool GUI group delay comparison to phase delay example grpdelay function passband grpdelay function example grpdelay method halfrange method hamming window function comparison to boxcar comparison to Hann example hann window function comparison to Hamming hanning See also hann window function highpass filters Butterworth Butterworth order Chebyshev Type I Chebyshev Type I order Chebyshev Type II Chebyshev Type II order elliptic elliptic order FIR FIR example lowpass transformation hilbert transform function analytic signals description example using firpls using firpm homomorphic systems icceps function example idct function example ideal lowpass filters See also lowpass filters ifft function example ifft2 function example IIR filters analog prototype Bessel Butterworth Chebyshev Type I Chebyshev Type II comparison comparison to FIR design elliptic Filter Designer GUI frequency domain implementation frequency response generalized Butterworth lattice/ladder Levinson-Durbin recursion maximally flat multiband order estimation plotting responses Prony's method specifications Steiglitz-McBride iteration yulewalk function Yule-Walker example zero-phase implementation See also direct design image processing impinvar function Import dialog box sptool from disk sptool from workspace impulse invariance example impulse response impz function ideal impulse invariance impz function impz method impzlength method indexing inf-norm info method dfilt function sigwin function initial conditions using dfilt states using filtfilt function using filtic function instantaneous attributes interpolation bandlimited FIR filters interp function interval notation intfilt function inverse cepstrum, complex inverse discrete cosine transforms accuracy of signal reconstruction inverse discrete Fourier transforms example matrices two-dimensional inverse filters analog discrete inverse Fourier transforms See also sinc function inverse-sine parameters transformations from reflection coefficients transformations to reflection coefficients invfreqs function example invfreqz function example is2rc function isallpass method iscascade method isfir method islinphase method ismaxphase method isminphase method isparallel method isreal method isscalar method issos method isstable method kaiser window function discussion example FIR filters kaiserord function ladder filters See also lattice/ladder filters Lagrange interpolation filter Laplace transforms lar2rc function latc2tf function example latcfilt function example lattice/ladder filters implementation latcfilt function Schur algorithm transfer functions conversions least squares method FIR levinson function example parametric modeling line drawing in FDATool line spectral frequencies transformation from prediction polynomial transformation to prediction polynomial line style linear models See also models linear phase filters least squares FIR optimal FIR linear prediction coefficients modeling linear system transformations See also conversions log area ratio parameters transformation from reflection coefficients transformation to reflection coefficients lowpass filters Bessel Butterworth Butterworth order Chebyshev Type I Chebyshev Type I order Chebyshev Type II Chebyshev Type II order cutoff frequency translation decimation elliptic elliptic order FIR ideal impulse invariance impulse response interpolation lp2bp function example lp2bs function lp2hp function lp2lp function lpc See also linear predictive coding, Prony's method, linear prediction lpc function lse lsf2poly function magnitude Fourier transforms frequency response extraction plots transfer functions match frequency prewarping MAT-files dpss.mat format, converting to importing sptool GUI matrices convolution convolution function data discrete Fourier transforms inverse discrete Fourier transforms matrix forms See also state-space forms maxflat function discussion maximally flat filters See also maxflat function maximum entropy estimate mean-square spectrum medfilt1 function example median filters See alsomedfilt1 function MEX-files M-files M-files minimax method FIR filters See also Parks-McClellan method minimum phase models autoregressive Burg autoregressive Burg PSD autoregressive covariance autoregressive covariance PSD autoregressive modified covariance autoregressive modified covariance PSD autoregressive Yule-Walker autoregressive Yule-Walker PSD bilinear transformations transformations modified covariance method modulate function modulate function definition example time vector See also amplitude modulation modulation moving-average (MA) filters See also FIR filters mscohere function msspectrum method msspectrumopts method MTM See also multitaper method multiband filters FIR IIR multichannel data multiple signal classification method (MUSIC) correlation matrices discussion eigenvector method example pseudospectrum multiplicity of zeros and poles multirate filters multitaper method (MTM) multi-taper spectrum object MUSIC algorithm See also multiple signal classification method MUSIC spectrum object nonrecursive filters See also FIR filters normalization cross-correlation modified periodogram periodogram bias Welch's power spectral density normalizefreq method nsections method nstages method nstate method nuttallwin Nuttall window function Nyquist frequency object changing properties copying dspdata dspopts filter filtstates filtstates spectrum viewing properties window onesided method options object order bit reversed Butterworth estimation Chebyshev Type I estimation digit reversed elliptic estimation estimation FIR optimal estimation order method oscillators overlap-add filter overlap-add method FIR filter implementation FIR filters Panner check box parallel method parametric modeling applications covariance method frequency domain based linear predictive coding modified covariance method Steiglitz-McBride method summary techniques time-domain based Yule-Walker method parentheses Parks-McClellan method partial fraction expansion residue z-transform parzenwin Parzen window function passband Chebyshev Type I equiripple group delay pburg function example PCM pcov function example peig function period in sequence periodic sinc functions See also Dirichlet functions periodogram function discussion spectrum object phase delay demodulation distortion Fourier transforms frequency response group delay linear delay modulation transfer functions unwrapping phase response phasedelay function phasez function phasez method plot method plots analog filters coherence function complex cepstrum DFT frequency response group delay magnitude magnitude and phase phase phase delays strip plots transfer functions zero-pole zplane functioin plug-ins pmcov function example p-model See also parametric modeling pmtm function pmusic function pole-zero editor pole-zero filters See also IIR filters poly function example poly2ac function poly2lsf function poly2rc function polynomials division roots scaling stability check stabilization polyphase filtering techniques polyscale function polystab function power spectral density Burg estimation Burg estimation example covariance estimation covariance estimation example dspdata object eigenvector stimation modified covariance estimation multitaper estimation multitaper estimation example MUSIC estimation MUSIC estimation example periodogram bias periodogram normalization plots sptool GUI units Welch's bias Welch's estimation Welch's estimation bias Welch's estimation example Welch's normalization Yule-Walker estimation Yule-Walker estimation example powerest method prediction filters prediction polynomials transformations from line spectral frequencies transformations to line spectral frequencies Preferences menu item prewarping Print dialog box prolate-spheroidal windows prony function example Prony's method See also prony function psd method psdopts method pseudospectrum object eigenvector method MUSIC algorithm pseudospectrumopts object pulse position demodulation pulse position modulation pulse time modulation pulse train generator pulse trains example Prony's method pulstran function pulse width demodulation pulse width modulation pulse-shaping filter pwelch function pyulear function Burg comparison example quadrature amplitude demodulation quadrature amplitude modulation quantization decoding encoding reduction with filter norms quantized filters cell arry coefficients matrix coefficients radar applications raised cosine filters range notation rc2ac function rc2is function rc2lar function rc2poly function rceps function example rceps function realizemdl method rebuffering rectangular windows rectwin function rectpuls function rectwin function example recursive filters See also IIR filters references general DSP special topics statistical signal processing reflection coefficients autocorrelation sequence conversion conversion from filter coefficients conversion to prediction polynomial definition Schur algorithm transformation from inverse sine parameters transformation from log area ratio parameters transformation to inverse sine parameters transformation to transformation to log area ratio parameters rejection area Remez exchange algorithm removestage method resample function example resampling See also decimation, interpolation residue forms See also partial fraction expansion residuez function rlevinson function rooteig function rootmusic function eigenvector method roots polynomials rulers sptool GUI sampling frequency sampling frequency decrease FIR filters freqz function increase integer factor decrease integer factor increase irregularly spaced data Nyquist interval range resample function resampling discussion spacing using upfirdn function saved filters saving data Spectrum Viewer Savitzky-Golay filters design filtering sawtooth function example sawtooth wave scaling Schur algorithm schurrc function second-order section forms zero-pole-gain conversion to second-order sections cell array coefficients conversion from transfer function conversion to in fdatool conversion to transfer functions filter filters matrices matrix coefficients sptool GUI state-space conversion from state-space conversion to view zero-pole-gain conversion from seqperiod function setstage method sgolay function sgolayfilt function Signal Browser axis labels markers preferences overview Panner preferences printing signals, measuring zooming, preferences signals adding noise analytic aperiodic applications array buffering carrier chirp continuous (analog) DCT coefficients reconstruction differentiators diric function discrete (digital) generating measurements minimum phase reconstruction example modulation multichannel periodic plotting properties pulstran function rebuffering representing sawtooth sawtooth function sinc sinusoidal square function square wave triangle sigwin function Simulink exporting from FDATool sinc function Dirichlet example Slepian sequences See also discrete prolate spheroidal sequences sonar applications sos method SOS view settings sos2cell function sos2ss function sos2tf function sos2zp function sosfilt function spectral analysis cross spectral density power spectrum Spectrum Viewer See also spectral estimation spectral density measurements plots Spectrum Viewer units See also power spectral density, cross spectral density spectral estimation AR covariance method AR modified covariance method AR Yule-Walker method Burg method Burg method example covariance method eigenvector method modified covariance method multitaper method MUSIC method periodograms root eigenvector root MUSIC Welch's method bias Welch's method discussion Welch's method example Yule-Walker AR method Yule-Walker AR method example spectrogram definition VCO example spectrogram function example spectrum mask spectrum estimation methods mean-square psd pseudospectrum spectrum function burg cov eigenvector estimation methods mcov methods mtm music periodogram welch yulear Spectrum Viewer activating axis parameters markers, preferences measurements opening overview printing rulers spectra structures spectral density plots windows zooming spectrum.mtm function example speech processing parametric modeling resampling spline function sptool GUI colors, customizing context-sensitive help customizing data entering data objects data structures editing example exporting data filter coefficients filter design filter importing filter parameters filter saving filtering filters help Import dialog importing filters and spectra importing signals items, selecting line style MAT-files MATLAB workspace multiselection of items operation preferences printing rulers sample frequency saving second-order section forms signal analysis signal measurement signal playing sound spectra analysis spectra import spectral densities import spectral densities plot Spectrum Viewer state-space forms transfer functions transfer functions export tutorial workspace zero-pole-gain forms square function example square wave See also square function ss method ss2sos function ss2tf function ss2zp function stability check polynomials stabilization standards, digital audio tape startup transients state-space forms continuous time scalar second-order section conversion from second-order section conversion to sptool GUI transfer functions conversions to zero-pole-gain conversion from zero-pole-gain convertion to statistical operations See also autocorrelation sequences, cross-correlation sequences, cross-covariance Steiglitz-McBride method example step response stepz method stepz function stmcb function example stopband Chebyshev Type II elliptic strips function plots structures conversion conversion round off lattice/ladder transposed direct-form II swept-frequency cosine generator See also chirp system identification tapers (PSD estimates) taps tf method tf2latc function example tf2sos function tf2ss function tf2zp function tfestimate function example time series attributes time-domain based modeling See also parametric modeling transfer functions coefficients discrete time models factoring lattice conversion to partial fractions second-order sections conversion from second-order sections conversion to sptool GUI state-space conversion to Welch's estimation zero-pole-gain forms transformations bilinear bilinear function frequency lowpass analog to bandpass lowpass analog to bandstop lowpass analog to highpass lowpass cutoff change models transforms chirp z-transforms (CZT) chirp z-transforms (CZT) discussion discrete cosine discrete Fourier hilbert Hilbert discussion inverse discrete cosine inverse discrete cosine discussion transients transition band transposed direct-form II initial conditions transposed direct-form II structure triang triangle window function Bartlett comparison tripuls function Tukey See also tukeywin Tukey window function tukeywin Tukey window function two-dimensional operations twosided method udecode function uencode function uniform encoding unit circle unit impulse function unit ramp function unit sample multichannel unit step function units of power spectral density (PSD) unwrap function example upfirdn function example resampling upsample function variables load from disk variance vco example vco function vectors data representation frequency indexing waveform generation weighting voltage controlled oscillators example waveforms See also signals Welch spectrum object Welch's method AR Yule-Walker comparison bias and normalization Burg comparison MTM comparison nonparametric system identification power spectral density estimation white noise wholerange method window function windows Bartlett Bartlett comparison Bartlett-Hanning Blackman Blackman comparison Blackman-Harris Blackman-Harris vs. Nuttall Bohman boxcar Chebyshev Chebyshev cosine de la Valle-Poussin designing filters FIR filters FIR filters multiband filters single band design fir1 function flat top weighted Gaussian Hamming Hamming discussion Hamming rectangular example Hamming ringing example Hann Hann example Kaiser Kaiser discussion Kaiser example Nuttall object Parzen prolate-spheroidal rectangular rectangular example shapes spectral leakage triangular Tukey viewing wintool GUI wvtool GUI wintool GUI winwrite method Workspace Contents list wvtool GUI xcorr function xcorr2 function xcov function yulewalk function example Yule-Walker AR method description example Welch's method comparison Yule-Walker spectrum object zero frequency component, centering zero-order hold See also averaging filters zero-phase filtering response zerophase function zerophase method zero-pole analysis multiplicity plots transfer functions zero-pole-gain zero-pole-gain forms convert from second-order sections convert from state-space convert to second-order sections convert to state-space sptool GUI zoom sptool GUI zp2sos function zp2ss function zp2tf function zpk method zplane function zplane method z-transforms chirp z czt function definition discrete Fourier transforms equation