Analytic signal & Hilbert transform (FFT) — Matlab/Python envelope
Build the analytic signal with Hilbert or FFT, extract envelope and instantaneous phase/frequency — Matlab, Python, and an interactive Hilbert demo.
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.
Histogram to PDF in Matlab — normalize bins and overlay the theoretical curve
Turn a Matlab histogram into an estimated PDF: normalize by sample count and bin width, then overlay normpdf / theoretical densities for Gaussian, Rayleigh, and exponential checks.
OFDM cyclic prefix length — how long must the CP be? (Matlab demo)
How long should the OFDM cyclic prefix be? CP must cover the channel delay spread so the FFT sees circular convolution — Matlab hands-on plus overhead calculator.
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 formula (root mean square) — definition, average power, and discrete signals
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 Eb/N0
Build AWGN from randn without Communications Toolbox: set noise variance from SNR or Eb/N0, generate real/complex noise, verify power.
Autocorrelation matrix in Matlab & Python — build R for Wiener / MVDR
Build the autocorrelation (covariance) matrix R from snapshots in Matlab or NumPy — including complex conjugate correlation — for Wiener, LMS, and MVDR beamformers.
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