Skip to main content
Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks

Fourier Spectral Analysis

 

We all know that for Fourier spectral analysis, you will get an impulse of significant magnitude at the frequency values of sine or cosine waves. Here, we will discuss the spectral analysis or frequency components when we add, subtract, multiply, convolve, integrate or differentiate signals, etc.

For sinusoidal signals

Addition

When we add two sinusoidal signals, the frequency components of the combined signal will be the frequencies of the individual signals. 





Subtraction

Again, for subtraction, the frequency components of the combined signal will be the frequencies of the individual signals. But if the amplitudes and periods for both signals are the same, then the combined signal will be null.

Multiplication

The frequency domain components for the time domain multiplication of two sinusoidal signals will be f1 ± f2, where f1 is the frequency of the first sinusoidal signal and f2 is for the other.

Convolution

The frequency domain components for the time-domain convolution of two sinusoidal signals will be centered at the original sinusoidal signal frequencies.

Differentiation

For a signal's differentiation, the signal's frequency components will be the same as the original signal, but its amplitude will be scaled by j.ω.

Integration

For integration of a signal, the frequency components of the signal will be the same as the original signal, but its amplitude will be scaled by 1 / j.ω

Further Reading

People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

profile

  Website: www.salimwireless.com
  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
  Seeking an opportunity in the Teaching or Electronics & Telecommunication domains.
  Possess M.Tech in Electronic Communication Systems.


Contact Us

Name

Email *

Message *

Popular Posts

MATLAB code for MSK

 Copy the MATLAB Code from here % The code is developed by SalimWireless.com clc; clear; close all; % Define a bit sequence bitSeq = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1]; % Perform MSK modulation [modSignal, timeVec] = modulateMSK(bitSeq, 10, 10, 10000); % Plot the modulated signal subplot(2,1,1); samples = 1:numel(bitSeq); stem(samples, bitSeq); title('Original message signal'); xlabel('Time (s)'); ylabel('Amplitude'); % Plot the modulated signal subplot(2,1,2); samples = 1:10000; plot(samples / 10000, modSignal(1:10000)); title('MSK modulated signal'); xlabel('Time (s)'); ylabel('Amplitude'); % Perform MSK demodulation demodBits = demodMSK(modSignal, 10, 10, 10000); % Function to perform MSK modulation function [signal, timeVec] = modulateMSK(bits, carrierFreq, baudRate, sampleFreq) % Converts a binary bit sequence into an MSK-modulated signal % Inputs: % bits - Binary input sequence % carrierFreq - Carri...
Read more

Difference between AWGN and Rayleigh Fading

Wireless Signal Processing Gaussian and Rayleigh Distribution Difference between AWGN and Rayleigh Fading 1. Introduction Rayleigh fading coefficients and AWGN, or additive white gaussian noise [↗] , are two distinct factors that affect a wireless communication channel. In mathematics, we can express it in that way.  Fig: Rayleigh Fading due to multi-paths Let's explore wireless communication under two common noise scenarios: AWGN (Additive White Gaussian Noise) and Rayleigh fading. y = h*x + n ... (i) Symbol '*' represents convolution. The transmitted signal  x  is multiplied by the channel coefficient or channel impulse response (h)  in the equation above, and the symbol  "n"  stands for the white Gaussian noise that is added to the signal through any type of channel (here, it is a wireless channel or wireless medium). Due to multi-paths the channel impulse response (h) changes. And multi-paths cause Rayleigh fa...
Read more

Constellation Diagrams of ASK, PSK, and FSK

BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1.    BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals: +√Eb​ or -√Eb (they differ by 180 degree phase shift), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  Key Points For Binary Amplitude Shift Keying (BASK), binary bit '0' can be represented as lower level voltage or no signal and bit '1' as higher level voltage.  For Binary Frequency Shift Keying (BFSK), you can map binary bit '0' to 'j' and bit '1' to '1'. So, signals are in phase.  A phase shift of 0 degrees could represent a binary '1...
Read more

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... What is Bit Error Rate (BER)? The abbreviation BER stands for bit error rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.   What is Signal the signal-to-noise ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance, the s...
Read more

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...   MATLAB Script for  BER vs. SNR for M-QAM, M-PSK, QPSk, BPSK %Written by Salim Wireless %Visit www.salimwireless.com for study materials on wireless communication %or, if you want to learn how to code in MATLAB clc; clear; close all; % Parameters num_symbols = 1e5; % Number of symbols snr_db = -20:2:20; % Range of SNR values in dB % PSK and QAM orders to be tested psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; % Initialize BER arrays ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); % BER calculation for each PSK order and SNR value for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) % Generate random symbols data_symbols = randi([0, psk_order-1], 1, num_symb...
Read more

Comparisons among ASK, PSK, and FSK | And the definitions of each

Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK Comparison among ASK,  FSK, and PSK Performance Comparison: 1. Noise Sensitivity:    - ASK is the most sensitive to noise due to its reliance on amplitude variations.    - PSK is less sensitive to noise compared to ASK.    - FSK is relatively more robust against noise, making it suitable for noisy environments. 2. Bandwidth Efficiency:    - PSK is the most bandwidth-efficient, requiring less bandwidth than FSK for the same data rate.    - FSK requires wider bandwidth compared to PSK.    - ASK's bandwidth efficiency lies between FSK and PSK. Bandwidth Calculator for ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second Select Modulation Type: ASK...
Read more

Fundamentals of Channel Estimation

Channel Estimation Techniques Channel Estimation is an auto-regressive process that may be performed with a number of iterations. There are commonly three types of channel estimation approaches. 1. Pilot estimation  2. Blind estimation  3. Semi-blind estimation. For Channel Estimation,  CIR [↗] is used. The amplitudes of the impulses decrease over time and are not correlated. For example, y(n) = h(n) * x(n) + w(n) where y(n) is the received signal, x(n) is the sent signal, and w(n) is the additive white gaussian noise At the next stage, h(n+1) = a*h(n) + w(n) The channel coefficient will be modified as stated above at the subsequent stage. The scaling factor "a" determines the impulse's amplitude, whereas "h(n+1)" represents the channel coefficient at the following stage. Pilot Estimation Method To understand how a communication medium is currently behaving, a channel estimate is necessary. In order to monitor a channel's behavior in practice communication ...
Read more

MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

  Pulse Amplitude Modulation (PAM) & Demodulation MATLAB Script clc; clear all; close all; fm= 10; % frequency of the message signal fc= 100; % frequency of the carrier signal fs=1000*fm; % (=100KHz) sampling frequency (where 1000 is the upsampling factor) t=0:1/fs:1; % sampling rate of (1/fs = 100 kHz) m=1*cos(2*pi*fm*t); % Message signal with period 2*pi*fm (sinusoidal wave signal) c=0.5*square(2*pi*fc*t)+0.5; % square wave with period 2*pi*fc s=m.*c; % modulated signal (multiplication of element by element) subplot(4,1,1); plot(t,m); title('Message signal'); xlabel ('Time'); ylabel('Amplitude'); subplot(4,1,2); plot(t,c); title('Carrier signal'); xlabel('Time'); ylabel('Amplitude'); subplot(4,1,3); plot(t,s); title('Modulated signal'); xlabel('Time'); ylabel('Amplitude'); %demdulated d=s.*c; % At receiver, received signal is multiplied by carrier signal filter=fir1(200,fm/fs,'low'); % low-pass FIR fi...
Read more