%% Waveform Generation
% The Signal Processing Toolbox provides functions for generating widely
% used periodic and aperiodic waveforms, sequences (impulse, step, ramp),
% multichannel signals, pulse trains, sinc and Dirichlet functions. This
% demo illustrates some of them.

%% Periodic Waveforms
% In addition to the *sin* and *cos* functions in MATLAB, the toolbox
% offers other functions that produce periodic signals such as sawtooth and
% square.
%
% The *sawtooth* function generates a sawtooth wave with peaks at ±1 and a
% period of 2*pi. An optional width parameter specifies a fractional
% multiple of 2*pi at which the signal's maximum occurs. 
%
% The *square* function generates a square wave with a period of 2*pi. An
% optional parameter specifies duty cycle, the percent of the period for
% which the signal is positive. 
%%
% To generate 1.5 seconds of a 50 Hz sawtooth (respectively square) wave with
% a sample rate of 10 kHz, use:
fs = 10000;
t = 0:1/fs:1.5;
x1 = sawtooth(2*pi*50*t);
x2 = square(2*pi*50*t);
subplot(211),plot(t,x1), axis([0 0.2 -1.2 1.2])
xlabel('Time (sec)');ylabel('Amplitude'); title('Sawtooth Periodic Wave')
subplot(212),plot(t,x2), axis([0 0.2 -1.2 1.2])
xlabel('Time (sec)');ylabel('Amplitude'); title('Square Periodic Wave')

%% Aperiodic Waveforms
% To generate triangular, rectangular and Gaussian pulses, the toolbox
% offers the tripuls, rectpuls and gauspuls functions.
%
% The *tripuls* function generates a sampled aperiodic, unity-height
% triangular pulse centered about t = 0 and with a default width of 1.
%
% The *rectpuls* function generates a sampled aperiodic, unity-height
% rectangular pulse centered about t = 0 and with a default width of 1.
% Note that the interval of non-zero amplitude is defined to be open on the
% right, that is, rectpuls(-0.5) = 1 while rectpuls(0.5) = 0. 
%%
% To generate 2 seconds of a triangular (respectively rectangular) pulse with
% a sample rate of 10 kHz and a width of 20 ms, use:
fs = 10000;
t = -1:1/fs:1;
x1 = tripuls(t,20e-3);
x2 = rectpuls(t,20e-3);
subplot(211),plot(t,x1), axis([-0.1 0.1 -0.2 1.2])
xlabel('Time (sec)');ylabel('Amplitude'); title('Triangular Aperiodic Pulse')
subplot(212),plot(t,x2), axis([-0.1 0.1 -0.2 1.2])
xlabel('Time (sec)');ylabel('Amplitude'); title('Rectangular Aperiodic Pulse')
set(gcf,'Color',[1 1 1]),
%%
% The *gauspuls* function generates a Gaussian-modulated sinusoidal pulse
% with a specified time, center frequency, and fractional bandwidth.
%
% The *sinc* function computes the mathematical sinc function for an input
% vector or matrix. The sinc function is the continuous inverse Fourier
% transform of the rectangular pulse of width 2*pi and height 1.
%%
% Generate a 50 kHz Gaussian RF pulse with 60% bandwidth, sampled at a rate of
% 1 MHz. Truncate the pulse where the envelope falls 40 dB below the peak:
tc = gauspuls('cutoff',50e3,0.6,[],-40); 
t1 = -tc : 1e-6 : tc; 
y1 = gauspuls(t1,50e3,0.6); 
%%
% Generate the sinc function for a linearly spaced vector:
t2 = linspace(-5,5);
y2 = sinc(t2);
%%
subplot(211),plot(t1*1e3,y1);
xlabel('Time (ms)');ylabel('Amplitude'); title('Gaussian Pulse')
subplot(212),plot(t2,y2);
xlabel('Time (sec)');ylabel('Amplitude'); title('Sinc Function')
set(gcf,'Color',[1 1 1]),

%% Swept-Frequency Waveforms
% The toolbox also provides functions to generate swept-frequency waveforms
% such as the *chirp* function. Two optional parameters specify alternative
% sweep methods and initial phase in degrees. Below are several examples of
% using the chirp function to generate linear or quadratic, convex and
% concave quadratic chirps.
%%
% Generate a linear chirp:
t = 0:0.001:2;                 % 2 secs @ 1kHz sample rate
ylin = chirp(t,0,1,150);       % Start @ DC, cross 150Hz at t=1sec
%%
% Generate a quadratic chirp:
t = -2:0.001:2;                % +/-2 secs @ 1kHz sample rate
yq = chirp(t,100,1,200,'q');   % Start @ 100Hz, cross 200Hz at t=1sec
%%
% Compute and display the spectrograms
subplot(211),spectrogram(ylin,256,250,256,1E3);
ylabel('Frequency'), title('Linear Chirp')
subplot(212),spectrogram(yq,128,120,128,1E3);
ylabel('Frequency'), title('Quadratic Chirp')
set(gcf,'Color',[1 1 1]);
%%
% Generate a convex quadratic chirp.
t = -1:0.001:1;                % +/-1 second @ 1kHz sample rate
fo=100; f1=400;                % Start at 100Hz, go up to 400Hz
ycx = chirp(t,fo,1,f1,'q',[],'convex');
%%
% Generate a concave quadratic chirp: 
t = -1:0.001:1;                % +/-1 second @ 1kHz sample rate
fo=400; f1=100;                % Start at 400Hz, go down to 100Hz
ycv=chirp(t,fo,1,f1,'q',[],'concave');
%%
% Compute and display the spectrograms
subplot(211),spectrogram(ycx,256,255,128,1000);
ylabel('Frequency'), title('Convex Chirp')
subplot(212),spectrogram(ycv,256,255,128,1000);
ylabel('Frequency'), title('Concave Chirp')
set(gcf,'Color',[1 1 1]);
%%
% Another function generator is the *vco* (Voltage Controlled Oscillator)
% which generates a signal oscillating at a frequency determined by the
% input vector. Let's look at two examples using vco with an triangle and
% rectangle input.
%
% Generate 2 seconds of a signal sampled at 10kHz whose instantaneous
% frequency is a triangle (respectively a rectangle) function of time: 
fs = 10000;
t = 0:1/fs:2;
x1 = vco(sawtooth(2*pi*t,0.75),[0.1 0.4]*fs,fs);
x2 = vco(square(2*pi*t),[0.1 0.4]*fs,fs);
%%
% Plot the spectrograms of the generated signals: 
subplot(211),spectrogram(x1,kaiser(256,5),220,512,fs);
ylabel('Frequency'), title('VCO Triangle')
subplot(212),spectrogram(x2,256,255,256,fs)
ylabel('Frequency'), title('VCO Rectangle')
set(gcf,'Color',[1 1 1]);

%% Pulse Trains
% To generate pulse trains, we can use the *pulstran* function. Below,
% we'll showcase two examples on how to use this function. 
%
% Construct a train of 2 GHz rectangular pulses sampled at a rate of 100
% GHz at a spacing of 7.5nS.
fs = 100E9;                    % sample freq
D = [2.5 10 17.5]' * 1e-9;     % pulse delay times
t = 0 : 1/fs : 2500/fs;        % signal evaluation time
w = 1e-9;                      % width of each pulse
yp = pulstran(t,D,@rectpuls,w);
%%
% Generate a periodic Gaussian pulse signal at 10 kHz, with 50% bandwidth.
% The pulse repetition frequency is 1 kHz, sample rate is 50 kHz, and pulse
% train length is 10msec. The repetition amplitude should attenuate by 0.8
% each time. The example uses a function handle to refer to the generator
% function.
T = 0 : 1/50E3 : 10E-3;
D = [0 : 1/1E3 : 10E-3 ; 0.8.^(0:10)]';
Y = pulstran(T,D,@gauspuls,10E3,.5); 
%%
subplot(211),plot(t*1e9,yp);axis([0 25 -0.2 1.2])
xlabel('Time (ns)'); ylabel('Amplitude'); title('Rectangular Train')
subplot(212),plot(T*1e3,Y)
xlabel('Time (ms)'); ylabel('Amplitude'); title('Gaussian Pulse Train')
set(gcf,'Color',[1 1 1]),
%%          
% Copyright 1988-2004 The MathWorks, Inc.