%% Raised Cosine Filtering
% This demonstration uses the Communications Toolbox functions, RCOSINE and
% RCOSFLT, to demonstrate the intersymbol interference rejection capability of
% the raised cosine filter.  It demonstrates how to use RCOSINE and RCOSFLT, how
% the raised cosine filter controls intersymbol interference, and how to split
% the raised cosine filtering between transmitter and receiver.

% Copyright 1996-2002 The MathWorks, Inc.
% $Revision: 1.19.2.1 $ $Date: 2003/04/23 06:13:42 $

%%
% This data sequence represents a digital sequence that will be upsampled by
% zero-padding before filtering.  Raised cosine filters will be used to shape
% the waveform without introducing intersymbol interference (ISI).

% Parameters.
Delay = 3; DataL = 20; R = .5; Fs = 8; Fd = 1; PropD = 0;
% Generate random data.
x = randsrc(DataL, 1, [], 1245);
% at time 0, 1/Fd, 2/Fd, ...
tx = [PropD: PropD + DataL - 1] ./ Fd;
% Plot data.
stem(tx, x, 'kx');
% Set axes and labels.
axis([0 30 -1.6 1.6]); xlabel('Time'); ylabel('Amplitude');

%%
% RCOSFLT is used to upsample and filter the data stream using the filter
% designed by RCOSINE.  The plot compares the digital data and the upsampled,
% filtered signal.  It is difficult to compare the two signals because the peak
% response of the filter is delayed by the group delay of the filter
% (order/(2*Fs)).

% Design filter.
[yf, tf] = rcosine(Fd, Fs, 'fir', R, Delay);
% Upsample and filter.
[yo, to] = rcosflt(x, Fd, Fs, 'filter', yf);
% Plot data.
stem(tx, x, 'kx'); hold on;
% Plot filtered data.
plot(to, yo, 'b-'); hold off;
% Set axes and labels.
axis([0 30 -1.6 1.6]);  xlabel('Time'); ylabel('Amplitude'); 

%%
% This step compensates for the raised cosine filter group delay by delaying the
% input signal.  Now it is easy to see how the raised cosine filter upsamples
% and filters the signal.  The filtered signal is identical to the delayed input
% signal at the input sample times.  This demonstrates the raised cosine filter
% capability to band-limit the signal while avoiding ISI.

% Correct for propagation delay
PropD = Delay * Fd;
% at time 0, 1/Fd, 2/Fd, ...
tx = [PropD: PropD + DataL - 1] ./ Fd;
% Plot data.
stem(tx, x, 'kx'); hold on;
% Plot filtered data.
plot(to, yo, 'b-'); hold off;
% Set axes and labels.
axis([0 30 -1.6 1.6]);  xlabel('Time'); ylabel('Amplitude');

%%
% This step demonstrates the effect that changing the rolloff factor from .5
% (blue curve) to .2 (red curve) has on the resulting filtered output.  The
% lower value for rolloff causes the filter to have a narrower transition band
% causing the filtered signal overshoot to be greater for the red curve than for
% the blue curve.
 
% Design filter.
[yg, tg] = rcosine(Fd, Fs, 'fir', .2, Delay);
% Filter data.
[yo1, to1] = rcosflt(x, Fd, Fs, 'normal/fir/filter',yg);
% Plot data.
stem(tx, x, 'kx'); hold on;
% Plot filtered data.
plot(to, yo, 'b-',to1, yo1, 'r-'); hold off;
% Set axes and labels.
axis([0 30 -1.6 1.6]);  xlabel('Time'); ylabel('Amplitude');

%%
% A typical use of raised cosine filtering is to split the filtering between
% transmitter and receiver.  The data stream is upsampled and filtered at the
% transmitter using the square-root raised cosine filter.  This plot shows
% the transmitted signal when filtered using the square-root raised cosine
% filter.  The "fir/sqrt" switch was used with RCOSINE to generate the
% square-root raised cosine filter.

% Design square root filter.
[ys, ts] = rcosine(Fd, Fs, 'fir/sqrt', R, Delay);
% Filter at the transmitter.
[yc, tc] = rcosflt(x, Fd, Fs, 'filter', ys);
% Plot data.
stem(tx, x, 'kx'); hold on;
% Plot filtered data.
plot(tc, yc, 'm-'); hold off;
% Set axes and labels.
axis([0 30 -1.6 1.6]);  xlabel('Time'); ylabel('Amplitude');

%%
% The transmitted signal (magenta curve) is then filtered, but not upsampled, at
% the receiver, using the same square-root raised cosine filter, resulting in a
% signal depicted by the blue curve at the receiver.  The resulting signal is
% virtually identical to the signal filtered using a single raised cosine
% filter.  The "Fs" was used to filter without upsampling.

% Filter at the receiver.
[yr, tr] = rcosflt(yc, Fd, Fs, 'filter/Fs', ys);
% Adjust for propagation delay.
tcc = tc + Delay .* Fd;  txx = tx + Delay .* Fd;
% Plot data.
stem(txx, x, 'kx'); hold on;
% Plot filtered data.
plot(tcc, yc, 'm-',tr, yr, 'b-'); hold off;
% Set axes and labels.
axis([0 30 -1.6 1.6]);  xlabel('Time'); ylabel('Amplitude');

%%
% This step demonstrates a quicker way to filter data using RCOSFLT.  When
% RCOSFLT is used without the "filter" type switch, it designs a filter and uses
% it to filter the input data.  This step creates the same plot as before but
% designs the raised cosine filter and generates the filtered stream in one
% command.

% Design and filter.
[yo2, to2] = rcosflt(x, Fd, Fs, 'normal/fir', R, Delay);
% Plot data.
stem(tx, x, 'kx'); hold on;
% Plot filtered data.
plot(to2, yo2, 'b-'); hold off;
% Set axes and labels.
axis([0 30 -1.6 1.6]);  xlabel('Time'); ylabel('Amplitude');