Signal Processing

Help with Signal Processing JohnDCook.com/DSP

A highpass filter cuts out low frequencies, i.e. it lets high frequencies pass.

Low-density parity-check codes en.wikipedia.org/wiki/Low-densi…

'It is good to choose coefficients to magnify the signal, but it is far better to choose them to cancel out the noise.' -- John Tukey

The sinc and jinc functions johndcook.com/blog/2012/02/0…

The real part of the Fourier transform of a real signal is an even function.

The Fourier transform of the discrete time impulse δ[n] is 1.

If sequences x and y have Fourier transforms X and Y, then the Fourier transform of x*y (i.e. x convolution y) is XY.

The Fourier transform of a convolution is the product of Fourier transforms.

The difference between two power levels, p and q, in decibels is 10 log_10(p/q).

Fourier uncertainty principle johndcook.com/blog/2021/03/1…

Since the DFT is almost always computed using the FFT, the two terms are used almost interchangeably.

The DFT is the discrete Fourier transform. The FFT is an algorithm for computing the DFT.

Shifting a sequence to the right by d multiplies its Fourier transform by exp(-2πi ω d).

If a sequence is square summable, its Fourier series converges in L2 norm.

Sound intensity en.wikipedia.org/wiki/Sound_int…

A periodic function has at least as many zeros at its lowest harmonic does. (Sturm-Hurwitz theorem) johndcook.com/blog/2021/01/1…

If a sequence is absolutely summable, its Fourier series converges uniformly.

Let h[n] be the impulse response in a linear time-invariant system. Then the response to a general signal x is x*h (convolution).

The convolution of two sequences x and y at a point n is the sum of the products x[k] y[n-k] over all integers k.

The discrete time impulse δ[n] is the sequence that equals 1 if n = 0 and equals 0 otherwise.