Generate AWGN in Matlab/Octave without awgn() — variance from Eb/N0
Build AWGN from randn without Communications Toolbox: set noise variance from SNR or Eb/N0, generate real/complex noise, verify power.
Signal Processing
Gold code generator — preferred pairs, correlation, and CDMA use
How Gold codes are built from preferred m-sequence pairs, their three-valued cross-correlation, and why they are used in CDMA/GNSS spreading.
Auto-Correlation Matrix in Matlab & Python: Toeplitz Form
Build the autocorrelation (covariance) matrix R from snapshots in Matlab or NumPy — including complex conjugate correlation — for Wiener, LMS, and MVDR beamformers.
Chirp signal spectrum — frequency sweep, FFT, and PSD (Matlab & Python)
Generate a linear chirp, view the spectrogram/FFT, and estimate PSD in Matlab or Python — how the instantaneous frequency sweep fills the spectrum.
Gaussian pulse and its PSD — generate, FFT, and spectrum shape
Generate a Gaussian pulse, compute its FFT/PSD, and see why a Gaussian time pulse has a Gaussian spectrum.
Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT
Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT). Often we are confronted with the need to generate simple, standard signals (sine, cosine, Gaussian pulse, square wave, isolated rectangular pulse, exponential decay, chirp signal) for simulation purpose. I intend to show (in a series of articles) … Read more
Square wave and its PSD — harmonics via FFT
Generate a square wave, take its FFT/PSD, and recognize the odd-harmonic 1/n envelope predicted by Fourier series.
Plot FFT of sine and cosine in Matlab — spectrum peaks done right
Matlab walk-through: sample a sinusoid, take FFT, build the frequency axis, and read peak locations — with Python twin link and FFT tool.
Sampling in Matlab and downsampling an audio file
Generating a continuous signal and sampling it at a given rate is demonstrated here. In simulations, we may require to generate a continuous time signal and convert it to discrete domain by appropriate sampling. For baseband signal, the sampling is straight forward. By Nyquist Shannon sampling theorem, for faithful reproduction of a continuous signal in … Read more
Shaping Randomness: A Guide to AR, MA, and ARMA Models
Key focus: AR, MA & ARMA models express the nature of transfer function of LTI system. Understand the basic idea behind those models & know their frequency responses. How do you describe a complex, random signal—like the sound of a human voice or the fluctuating power of a fading channel—using only a few numbers? The … Read more