Abstract: In a spectrum analyzer, the analogue signal to be analyzed is periodically sampled and digitized, and the digit samples are formed into R successive arrays each containing 2N successive samples and each overlapping the previous array by 50%. The forward Fourier transforms of each array are then successively formed, and an array of 2P complex points is formed from the result of each transform, where L-P/2 and L+P/2-1 are the points which represent the upper and lower limits of a Vernier band to be studied in detail and each array extends from points L-P to L+P-1 (i.e. each array is twice the width of the Vernier band, and the Vernier band is symmetrically disposed therein): additionally, each array for which L and R are odd is complemented. The arrays thus formed are then each multiplied by a window function (effectively equivalent to a band pass filter), and the result is subjected to the inverse Fourier transform to form respective further arrays of 2P points.