Signal Processing Formulas
Signal processing formulas for Nyquist sampling rate, Fourier transform, filter design, convolution, and frequency spectrum analysis.
Fourier Transform
Reference for the continuous Fourier Transform X(f) = ∫ x(t) e^(-i2πft) dt. Converts time-domain signals to frequency spectra. Foundation of DSP.
Nyquist-Shannon Sampling Theorem
Reference for Nyquist-Shannon: sampling rate must be at least 2× bandwidth to avoid aliasing. Covers anti-aliasing filters and audio recording at 44.1 kHz.
Z-Transform
Reference for the Z-transform X(z) = Σ x[n] z^(-n). Generalizes the discrete Fourier transform for digital filter design and analysis.