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.
Tutorials
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.
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.
Compute signal power in Matlab
Calculating the energy and power of a signal was discussed in one of the previous posts. Here, we will verify the calculation of signal power using Discrete Fourier Transform (DFT) in Matlab. Check here to know more on the concept of power and energy. The total power of a signal can be computed using the … Read more
Signal power vs energy — formulas and Matlab/Python examples
Power vs energy of a signal: finite-energy vs finite-power classification, discrete formulas, and Matlab/Python checks before BER or PSD normalization.
FFT spectral leakage — causes, scalloping, and how windows help
Why FFT bins leak when tones miss bin centers, what scalloping loss is, and how windowing + ENBW trade leakage against noise bandwidth.