Skip to main content

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
🎓 GATE SOLUTIONS
📡 WIRELESS & THEORY

Contact Us

Name

Email *

Message *

Popular Posts

Q-function in BER vs SNR Calculation

Q-function in BER vs. SNR Calculation In digital communications and signal processing, the Q-function plays a significant role in predicting system reliability. It allows engineers to quantify the probability that Gaussian noise will exceed a specific threshold, causing a bit error. What is the Q-function? The Q-function is a mathematical function representing the tail probability of the standard normal (Gaussian) distribution. It is the complementary cumulative distribution function (CCDF) of a standard Gaussian distribution. Q(x) = (1 / √(2Ï€)) ∫â‚“∞ e^(-t² / 2) dt Q-Function Interactive Simulator Move the slider to see how the "Tail Probability" (the area in red) changes. This area represents the Probability of Error (BER) . Threshold Distance ( x ) — (Simulates Increasing SNR) x = 1.0 Q(x) = 0.1587 ...
Read more

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 📘 Theory 🧮 Simulators 💻 MATLAB Code 📚 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 📂 Explore M-ary QAM, PSK, and QPSK Topics ▼ 🧮 Constellation Simulator: M-ary QAM 🧮 Constellation Simulator: M-ary PSK 🧮 BER calculation for ASK, FSK, and PSK 🧮 Approaches to BER vs SNR What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figure of merit f...
Read more

RMS Delay Spread, Excess Delay Spread and Multi-path ...(with MATLAB + Simulator)

📘 Overview of Delay Spread and Multi-path 🧮 Excess Delay spread 🧮 Power delay Profile 🧮 RMS Delay Spread 📚 Further Reading 📂 Other Topics on RMS Delay Spread, Excess Delay ... 🧮 Multipath Components or MPCs 🧮 Online Simulator for Calculating RMS Delay Spread 🧮 Why is there significant multipath in the case of very high frequencies? 🧮 Why RMS Delay Spread is essential for wireless communication? 🧮 Why the Power Delay Profile is essential? 🧮 MATLAB Codes for Calculating Different Types of delay Spreads Delay Spread, Excess Delay Spread, and Multipath (MPCs) The fundamental distinction between wireless and wired connections is that in wireless connections signal reaches at receiver thru multipath signal propagation rather than directed transmission like co-axial cable. Wireless Communication has no set communication path between the transmitter and the receiver. The line...
Read more

FM Bandwidth and FM Band Explained

FM radio uses the frequency band from 88 MHz to 108 MHz , which is a 20 MHz-wide spectrum . This is the range of carrier frequencies available to stations. 108 MHz − 88 MHz = 20 MHz However, a single FM station occupies only about 200 kHz . This is the bandwidth of the modulated FM signal. 1. Why One FM Station Needs ~200 kHz FM uses frequency modulation . The bandwidth depends on how far the carrier swings. Carson's Rule gives the approximate FM bandwidth: B = 2 ( Δf + f m ) ...
Read more

OFDM Symbols and Subcarriers Explained

This article explains how OFDM (Orthogonal Frequency Division Multiplexing) symbols and subcarriers work. It covers modulation, mapping symbols to subcarriers, subcarrier frequency spacing, IFFT synthesis, cyclic prefix, and transmission. Step 1: Modulation First, modulate the input bitstream. For example, with 16-QAM , each group of 4 bits maps to one QAM symbol. Suppose we generate a sequence of QAM symbols: s0, s1, s2, s3, s4, s5, …, s63 Step 2: Mapping Symbols to Subcarriers Assume N sub = 8 subcarriers. Each OFDM symbol in the frequency domain contains 8 QAM symbols (one per subcarrier): Mapping (example) OFDM symbol 1 → s0, s1, s2, s3, s4, s5, s6, s7 OFDM symbol 2 → s8, s9, s10, s11, s12, s13, s14, s15 … OFDM sym...
Read more

Frequency Shift Keying (FSK) Modulation & Demodulation (with Simulation)

Frequency Shift Keying (FSK) Theoretical Foundations: Frequency Shift Keying (FSK) is a discrete frequency modulation scheme wherein the digital information is encoded via instantaneous shifts in the carrier signal's frequency. The fundamental implementation is Binary FSK (BFSK), which maps binary data onto two distinct, discrete spectral states. A binary '1' (the "mark" state) is represented by a carrier frequency \( f_1 \), while a binary '0' (the "space" state) corresponds to frequency \( f_2 \). Each symbol is sustained for a bit interval denoted by \( T_b \). FSK Transmitter Characterization: The mathematical model for the modulated BFSK output \( s(t) \) is defined as: \[ s(t) = \begin{cases} A_c \cos(2\pi f_1 t), & \text{for } m = 1 \\ A_c \cos(2\pi f_2 t), & \text{for } m = 0 \end{cases} \] ...
Read more

Orthogonal Time Frequency Space (OTFS) (with MATLAB)

In OTFS (Orthogonal Time Frequency Space) modulation — a scheme designed for high-Doppler and time-varying wireless channels — the terms ISFFT and SFFT are key mathematical transformations used to move between different representation domains. Figure: OTFS block diagram 1. ISFFT — Inverse Symplectic Finite Fourier Transform Purpose: Transforms data symbols from the delay-Doppler domain to the time-frequency domain . \[ X[n, m] = \frac{1}{\sqrt{NM}} \sum_{k=0}^{N-1} \sum_{l=0}^{M-1} x[k, l] \, e^{j2\pi \left( \frac{nk}{N} - \frac{ml}{M} \right)} \] Here, \( N \) is the number of Doppler bins (time slots), and \( M \) is the number of delay bins (subcarriers). The ISFFT maps each data symbol from the delay-Doppler grid (where the channel is sparse and easier to equalize) to the time-frequency grid (where standard multicarrier modulation like OFDM can be applied). 2. SFFT — Symplectic Finite Fourier Transform Purpose: Performs the reverse operation ...
Read more