A general formula is derived for the spectrum of a multiply‐periodic, amplitude modulated sequence of pulses. The result is used to show that a function which lies in a frequency band (W0,W0+W) is completely determined by its values at a properly chosen set of points of density 2W. This verifies a supposition commonly accepted in communication theory.The well‐known, exact interpolation formula for a functionf(t) in a band (O, W) isf(t)=&Sgr;nf(n/2W)sin&pgr;(2Wt−n)&pgr;(2Wt−n).The function is thus determined by its values at a set of evenly spaced points ½Wapart.For a functionf(t) in a band (W0,W0+W) it is shown that an exact interpolation formula isf(t)=&Sgr;n[f(n/W)s(t−n/W)+f(n/W+k)s(n/W+k−t)]in whichkis subject to weak restrictions ands(t)=cos[2&pgr;(W0+W)t−(r+1)&pgr;Wk]−cos[2&pgr;(rW−W0)t−(r+1)&pgr;WK]2&pgr;Wtsin(r+1)&pgr;WK+cos[2&pgr;(rW−W0)t−r&pgr;Wk]−cos[2&pgr;W0t−r&pgr;Wk]2&pgr;Wtsinr&pgr;Wk.Thus, the function is determined by its values at a set of points of density 2W, but the points consist of two similar groups with spacing 1/W, shifted with respect to each other.