Skip to main content

What should be the relationship among the message, carrier, and sampling frequencies?

 

Nyquist-Shannon sampling theorem only says that your sampling frequency should be greater than twice the bandwidth of the signal. For example, you can modulate your 20 MHz signal at any carrier frequency you need and still get back your original signal by sampling at greater than 40 MHz.

Another example, Voice bandwidth is around 330 Hz to 3.3 KHz. For easy mathematics, we usually band limit it at 4 KHz or better known as Fmax. By Nyquist sampling Theorem, to prevent Aliasing, Sampling frequency (Fs) must be at least 2 times of Fmax.

Thus Fs >= 2*Fmax or 8 KHz.

On the other hand, if you are transmitting a signal of bandwidth B Hz, then the carrier frequency should be significantly greater than B Hz. In practical terms, the carrier frequency is often several times (5-10 times or more) higher than the bandwidth of the message signal to ensure that the modulation process is efficient and can be easily recovered at the receiver.  

In general, in most practical communication systems, the sampling frequency is usually greater than the carrier frequency. You can also read about why the sampling frequency should be greater than the carrier frequency. Given these considerations, the sampling frequency is usually designed to meet the Nyquist criterion for the message signal's bandwidth, which often results in a sampling frequency that is higher than the carrier frequency.

Therefore, the sampling frequency must be equal to or greater than twice the highest frequency component (or bandwidth) available in the message signal. Thus, 100 times the frequency of the message signal can be chosen for sampling, and 10 times the frequency of the message signal can be chosen for the carrier signal. Permit the user to choose the frequency of the message signal and adjust the sampling frequency accordingly.

For additional information and MATLAB code, see this article by clicking here

 

People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

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

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR 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. BER = (number of bits received in error) / (total number of tran...

Constellation Diagrams of ASK, PSK, and FSK

📘 Overview of Energy per Bit (Eb / N0) 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory behind Constellation Diagrams of ASK, FSK, and PSK 🧮 MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK 📚 Further Reading 📂 Other Topics on Constellation Diagrams of ASK, PSK, and FSK ... 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM 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...

MATLAB Code for ASK, FSK, and PSK

📘 Overview & Theory 🧮 MATLAB Code for ASK 🧮 MATLAB Code for FSK 🧮 MATLAB Code for PSK 🧮 Simulator for binary ASK, FSK, and PSK Modulations 📚 Further Reading ASK, FSK & PSK HomePage MATLAB Code MATLAB Code for ASK Modulation and Demodulation % The code is written by SalimWireless.Com % Clear previous data and plots clc; clear all; close all; % Parameters Tb = 1; % Bit duration (s) fc = 10; % Carrier frequency (Hz) N_bits = 10; % Number of bits Fs = 100 * fc; % Sampling frequency (ensure at least 2*fc, more for better representation) Ts = 1/Fs; % Sampling interval samples_per_bit = Fs * Tb; % Number of samples per bit duration % Generate random binary data rng(10); % Set random seed for reproducibility binary_data = randi([0, 1], 1, N_bits); % Generate random binary data (0 or 1) % Initialize arrays for continuous signals t_overall = 0:Ts:(N_bits...

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

🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together 🧮 MATLAB Code for M-ary QAM 🧮 MATLAB Code for M-ary PSK 📚 Further Reading MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK % Written by Salim Wireless clc; clear; close all; num_symbols = 1e5; snr_db = -20:2:20; psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) data_symbols = randi([0, psk_order-1], 1, num_symbols); modulated_signal = pskmod(data_symbols, psk_order, pi/psk_order); received_signal = awgn(modulated_signal, snr_db(j), 'measured'); demodulated_symbols = pskdemod(received_signal, psk_order, pi/psk_order); ber_psk_results(i, j) = sum(data_symbols ~= demodulated_symbols) / num_symbols; end end for i...

Theoretical vs. simulated BER vs. SNR for ASK, FSK, and PSK

📘 Overview 🧮 Simulator for calculating BER 🧮 MATLAB Codes for calculating theoretical BER 🧮 MATLAB Codes for calculating simulated BER 📚 Further Reading BER vs. SNR denotes how many bits in error are received for a given signal-to-noise ratio, typically measured in dB. Common noise types in wireless systems: 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading AWGN adds random noise; Rayleigh fading attenuates the signal variably. A good SNR helps reduce these effects. Simulator for calculating BER vs SNR for binary ASK, FSK, and PSK Calculate BER for Binary ASK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary FSK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary PSK Modulation Enter SNR (dB): Calculate BER BER vs. SNR Curves MATLAB Code for Theoretical BER % The code is written by SalimWireless.Com clc; clear; close all; % SNR va...

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

📘 Comparisons among ASK, FSK, and PSK 🧮 Online Simulator for calculating Bandwidth of ASK, FSK, and PSK 🧮 MATLAB Code for BER vs. SNR Analysis of ASK, FSK, and PSK 📚 Further Reading 📂 View Other Topics on Comparisons among ASK, PSK, and FSK ... 🧮 Comparisons of Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Online Simulator for ASK, FSK, and PSK Generation 🧮 Online Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers 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 Parameters ASK FSK PSK Variable Characteristics Amplitude Frequency ...

MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK

📘 Overview & Theory 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Online Simulator for Constellation diagrams of ASK, FSK, and PSK 📚 Further Reading   MATLAB Script % The code is developed by SalimWireless.Com clc; clear; close all; % Parameters numSymbols = 1000; % Number of symbols to simulate symbolIndices = randi([0 1], numSymbols, 1); % Random binary symbols (0 or 1) % ASK Modulation (BASK) askAmplitude = [0, 1]; % Amplitudes for binary ASK askSymbols = askAmplitude(symbolIndices + 1); % Modulated BASK symbols % FSK Modulation (Modified BFSK with 90-degree offset) fs = 100; % Sampling frequency symbolDuration = 1; % Symbol duration in seconds t = linspace(0, symbolDuration, fs*symbolDuration); fBase = 1; % Base frequency frequencies = [fBase, fBase]; % Same frequency for both % Generate FSK symbols with 90° phase offset fskSymbols = arrayfun(@(idx) ...     cos(2*pi*frequencies(1)*t) * (1-idx) + ...     ...

DSB-SC Modulation and Demodulation

📘 Overview 🧮 DSB-SC Modulator 🧮 DSB-SC Detector 🧮 Comparisons Between DSB-SC and SSB-SC 🧮 Q & A and Summary 📚 Further Reading   Double-sideband suppressed-carrier transmission (DSB-SC) is transmission in which frequencies produced by amplitude modulation (AM) are symmetrically spaced above and below the carrier frequency and the carrier level is reduced to the lowest practical level, ideally being completely suppressed. In the DSB-SC modulation, unlike in AM, the wave carrier is not transmitted; thus, much of the power is distributed between the sidebands, which implies an increase of the cover in DSB-SC, compared to AM, for the same power use. DSB-SC transmission is a special case of double-sideband reduced carrier transmission. It is used for radio data systems. This model is frequently used in Amateur radio voice communications, especially on High-Frequency ba...