Analysis of samples of wideband signals taken at irregular, sub-Nyquist, intervals

A modified discrete Fourier transform is stated for estimating the spectrum of a signal sampled at irregular intervals. Additive pseudorandom sampling is proposed as an irregular sampling scheme. The transform periodicity and symmetrical properties are derived for the scheme. Alias-free spectral analysis of a bandlimited periodic signal is possible when using additive pseudorandom sampling with a maximum sampling rate below that specified by the Nyquist criterion.