Frequency-response estimates using discrete signals and the radix-2 f.f.t.

Large errors occur when using pseudorandom binary sequences and the radix-2 fast Fourier transform (f.f.t.) to estimate the frequency response of linear systems. The reason for this phenomenon is discussed and it is shown that using an augmented p.r.b.s. accurate estimates of frequency responses can be made with the radix-2 f.f.t. Augmented p.r.b.s. has a further advantage, namely that of a zero mean level. This feature is particularly important when identifying systems with free integrators (type 1 systems), as a small bias in the test signal can cause gross errors in the estimates. It is shown that discrete frequency-response estimates are identical (in the absence of noise) for all discrete test signals, periodic in the data window length. However, by utilising a test signal which has a small number of harmonic components relative to the number of samples in the generated signal, the input and output of the system may be sampled at a much reduced rate without compromising accuracy. Thus equally accurate estimates can be made with a significantly reduced computation time and storage requirement.