### Common digital signal processing questions

### Fourier transform and its properties

Representation of periodic signals by the Fourier series

Spectrum of a rectangular pulses periodic sequence

Fourier transform of a nonperiodic signal

Spectrums of some nonperiodic signals

Energy characteristics of signals. Energy spectrum

Dirac delta function and its properties

Fourier transform of non-integrable signals

### Discrete Fourier Transform

Discrete-time Fourier transform (DTFT)

Discrete Fourier Transform (DFT)

The relationship between DTFT and DFT. Dirichlet kernel

Discrete Fourier transform spectral samples indexing and rearranging

### Algorithms for Discrete Fourier Transform

Fast Fourier Transform. Main idea

Radix-2 FFT decimation in time

Radix-2 FFT decimation in frequency

### Analog and Digital Filters

Laplace transform and it properties

Using the Laplace operator to describe electrical circuits

Analog normalized Butterworth low-pass filter

Analog normalized Chebyshev low-pass filter of the first kind

Analog normalized Chebyshev low-pass filter of the second kind

Analog normalized elliptic low-pass filter

Analog filter frequency transforms. LPF-LPF and LPF-HPF

Laplace transform of a discrete signal.

Z-transform. Discrete-time filter difference equation

DSPL-2.0 is free digital signal processing algorithms library

Distributed under LGPL v3 license

project page on GitHub

### Digital Resampling

Digital resampling based on polynomial interpolation. Farrow filter

Farrow filter applications based on polynomial interpolation

### Signals theory

Hilbert transform. Analytical signal

Analytic signal genration based on a quadrature mixer

Bandpass radio signals. Complex envelope and quadrature modulator

The complex envelope recovery. Quadrature receiver

Quadrature receiver with random initial phase and frequency detuning

Amplitude Modulation (AM). Double side band modulation (DSB)

Single side band modulation (SSB)

Frequency (FM) and phase (PM) modulations

Demodulation of FM and PM signals

Frequency shift keying modulation (FSK) and continuous phase FSK (CPFSK)

Minimum shift keying (MSK) modulation