Interpolate and Decimate Using RRC Filter

This example shows how to interpolate and decimate signals using square-root, raised cosine filters designed with the rcosdesign function. This example requires the Communications Toolbox™ software.

Define the square-root raised cosine filter parameters. Define the signal constellation parameters.

rolloff = 0.25; % Filter rolloff
span = 6;       % Filter span
sps = 4;        % Samples per symbol
M = 4;          % Size of the signal constellation
k = log2(M);    % Number of bits per symbol

Generate the coefficients of the square-root raised cosine filter using the rcosdesign function.

rrcFilter = rcosdesign(rolloff,span,sps);

Generate 10000 data symbols using the randi function.

data = randi([0 M-1],10000,1);

Apply PSK modulation to the data symbols. Because the constellation size is 4, the modulation type is QPSK.

modData = pskmod(data,M,pi/4);

Using the upfirdn function, upsample and filter the input data.

txSig = upfirdn(modData,rrcFilter,sps);

Convert the Eb/N0 to SNR and then pass the signal through an AWGN channel.

EbNo = 7;
snr = EbNo + 10*log10(k) - 10*log10(sps);
rxSig = awgn(txSig,snr,'measured');

Filter and downsample the received signal. Remove a portion of the signal to account for the filter delay.

rxFilt = upfirdn(rxSig,rrcFilter,1,sps);
rxFilt = rxFilt(span+1:end-span);

Create a scatterplot of the modulated data using the first 5000 symbols.

hScatter = scatterplot(sqrt(sps)* ...
    rxSig(1:sps*5000), ...
    sps,0);
hold on
scatterplot(rxFilt(1:5000),1,0,'bx',hScatter)
title('Received Signal, Before and After Filtering')
legend('Before Filtering','After Filtering')
axis([-3 3 -3 3]) % Set axis ranges
hold off