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Raised Cosine Filter in MATLAB (with Simulator)


 

MATLAB Code

clc;
clear all; close all;
Data_sym = [0 1 1 0 1 0 0 1];
M = 4;
Phase = 0;
Sampling_rate = 48e3;
Data_Rate = 100;
Bandwidth = 400;
Upsampling_factor = Sampling_rate/Data_Rate;
Rolloff = 0.4;
Upsampled_Data = upsample(pskmod(Data_sym,M,Phase),Upsampling_factor);
Pulse_shape = firrcos(2*Upsampling_factor,Bandwidth/2,Rolloff,Sampling_rate,'rolloff','sqrt');

Output

What if we change the roll-off

roll-off = 0.01



roll-off = 0.99




What if we change the bandwidth

Bandwidth = 100 Hz

 
 
Bandwidth = 1000 Hz 
 


What if we change the sampling rate

 Sampling rate = 10 KHz


 Sampling rate = 100 KHz



Another MATLAB Code

% The code is developed by SalimWireless.Com
clc;
clear;
close all;

% Parameters
fs = 1000; % Sampling frequency in Hz
symbolRate = 100; % Symbol rate (baud)
span = 6; % Filter span in symbols
alpha = 0.25; % Roll-off factor for raised cosine filter


% Generate random data symbols
numSymbols = 100; % Number of symbols
data = randi([0 1], numSymbols, 1) * 2 - 1; % Generate random binary data (BPSK symbols: -1, 1)

% Upsample the data to match sampling rate
samplesPerSymbol = fs / symbolRate; % Samples per symbol based on fs and symbol rate
dataUpsampled = upsample(data, samplesPerSymbol);

% Create a raised cosine filter
rcFilter = rcosdesign(alpha, span, samplesPerSymbol, 'sqrt'); % Square root raised cosine filter

% Apply the filter to the upsampled data
txSignal = conv(dataUpsampled, rcFilter, 'same');

figure;
subplot(4,1,1)
stem(data);
title('Original Message signal');
grid on;

subplot(4,1,2)
plot(dataUpsampled);
title('Upsampled Message signal');
grid on;

subplot(4,1,3)
plot(rcFilter);
title('Raise Cosine Filter Coefficient');
grid on;

subplot(4,1,4)
plot(txSignal);
title('Transmitted Signal after Raised Cosine Filtering');
grid on;
 

Output

 

 
 
 
 

Copy the MATLAB Code above from here

 

 


Raised Cosine Filter Online Simulator

Random Bits
   ↓
BPSK Mapping (±1)
   ↓
Upsampling
   ↓
RRC (Root Raised Cosine) Filter Pulse Shaping



Simulation Note: The simulator generates random BPSK symbols, applies pulse shaping using a Root Raised Cosine (RRC) filter with roll-off factor β , adds AWGN noise, and detects symbols using a matched filter.
Lower β values use less bandwidth but pulses are narrower in time and more susceptible to inter-symbol interference (ISI). Higher β values spread the pulse in time but reduce ISI and require more bandwidth.

Raised Cosine Filter: Basics, Formula, etc.

In wireless communication, Raised Cosine Filters (RCF) are essential for pulse shaping. Their primary goal is to minimize Inter-Symbol Interference (ISI) by ensuring the transmitted waveform fits within a specific bandwidth while maintaining timing accuracy at the receiver.

Key Formula & Bandwidth Calculation

The bandwidth ($B$) of a raised cosine filter is determined by the symbol rate ($R_s$) and the roll-off factor ($\alpha$), which ranges from 0 to 1:

Bandwidth (B) = [Symbol Rate × (1 + α)] / 2

Example: For a symbol rate of 100 symbols/sec and a roll-off factor ($\alpha$) of 0.25:
B = [100 × (1 + 0.25)] / 2 = 62.5 Hz.
This slightly exceeds the theoretical Nyquist minimum (50 Hz) to allow for realistic filter implementation without ISI.

Applications in Modern Systems

  • Time-Bandwidth Product (TBP): RCFs help manage the trade-off between time localization and spectral efficiency. Higher $\alpha$ reduces ISI but increases the TBP.
  • OFDM Systems: Pulse shaping confines the spectral bandwidth of OFDM waveforms, reducing out-of-band emissions and adjacent channel interference.
  • Pulse Shaping: Essential for mapping digital bits to analog waveforms suitable for band-limited channels.

Read more

Further reading

 
📊 MATLAB & ONLINE SIMULATIONS (Web-Based)
🎓 GATE & UGC - NET SOLUTIONS
📡 WIRELESS & SIGNAL PROCESSING


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