Analytic signal, Hilbert transform, and FFT — envelope and instantaneous phase
How the analytic signal and Hilbert transform give envelope and instantaneous phase/frequency, FFT implementation tips, and links to the envelope follow-on.
Tips & Tricks
FIR vs IIR filters — how to choose for your design
FIR vs IIR tradeoffs: linear phase, stability, order, and when each wins — with links to digital filter design articles.
Plot histogram and estimated PDF in Matlab
Key focus: With examples, let’s estimate and plot the probability density function of a random variable using Matlab histogram function. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability density function … Read more
Cyclic prefix in OFDM — circular convolution and a Matlab hands-on demo
OFDM study path — 5 lessons (same on every page in this series) 1. Introduction → 2. Orthogonality → 3. IFFT modem → 4. Cyclic prefix (you are here) → 5. BER in AWGN Tools: OFDM CP overhead calculator · Eb/N0 ↔ SNR converter In one sentence: A cyclic prefix tricks a natural (linear) … Read more
FFT magnitude and phase spectrum — how to interpret (and fix noisy phase)
How to get amplitude and phase from an FFT: |X[k]|, atan2, why phase looks noisy, the magnitude threshold fix, Matlab + Python, and links to bins/fftshift and the FFT calculator.
Interpret FFT results — complex DFT, frequency bins, and fftshift
How DFT bins map to Hz, what negative frequencies mean, when to use fftshift/ifftshift, and how this pairs with magnitude/phase plots.
RMS (root mean square) value — meaning, formula, and signal power
What RMS means for voltages and DSP signals, how it ties to average power, and the formulas for continuous and discrete waveforms.
Generate AWGN in Matlab/Octave without awgn() — variance from SNR
Create AWGN manually: set noise variance from SNR or Eb/N0, generate real/complex noise, and verify power — links to BER tools.
Construct autocorrelation Matrix in Matlab & Python
Auto-correlation, also called series correlation, is the correlation of a given sequence with itself as a function of time lag. Cross-correlation is a more generic term, which gives the correlation between two different sequences as a function of time lag. Given two sequences $latex x$ and $latex y$, the cross-correlation at times separated by lag … Read more
QAM Modulation using Karnaugh-map walks
This article focused on constructing constellation for rectangular QAM modulation using Karnaugh-map walks. Exploit inherent property of Karnaugh-maps to construct Gray coded QAM constellation points. M-ary Quadrature Amplitude Modulation (M-QAM) In MQAM modulations, the information bits are encoded as variations in the amplitude and the phase of the signal. The M-QAM modulator transmits a series … Read more