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Frequency Translation of a Sampled Signal

IP.com Disclosure Number: IPCOM000084490D
Original Publication Date: 1975-Nov-01
Included in the Prior Art Database: 2005-Mar-02
Document File: 3 page(s) / 40K

Publishing Venue

IBM

Related People

Choquet, M: AUTHOR

Abstract

Shown is a circuit to permit the frequency translation of a sampled signal to be performed, on condition that the sampling frequency F = 1/T be an integer multiple of translation frequency f(t)

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Frequency Translation of a Sampled Signal

Shown is a circuit to permit the frequency translation of a sampled signal to be performed, on condition that the sampling frequency F = 1/T be an integer multiple of translation frequency f(t)

Frequency translation of a signla x(t) consists in modulating signal x(t) with a sine wave, the frequency of which is equal to f(t), and selecting the wanted spectrum among the two spectra with carrier frequency f(t) + fc and f(t) - fc, fc being the carrier frequency of signal x(t). Assuming x(t) to be the Hilbert transform of signal x(t) and f(t) to be a higher frequency than the upper band of frequency spectrum of x(t), the translated signal y(t) is expressed by: y(t) = x(t) cos 2 phi f(t) t + Esp. x(t) sin 2 pi f(t) t.

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With the sampling frequency being an integer multiple k of translation frequency f(t), the values taken by c(iT) and s(iT) and s(iT) have to be calculated at particular instants of the period 1/f (f) of the cosine wave and the sine wave. Consequently, depending upon the value of k, output samples of the translated signal may be easily calculated. The illustrated logic circuit allows the translation operation to be performed with k equal to 4, which gives for c(t0 and s(iT) the following values during a period equal to 4T: c(4iT) = 1 c(4i + 1)T = 0 c(4i + 2)T = -1 c(4i + 3)T = 0 s(4iT) = 0 s(4i + 1)T = 1 s(4i + 2)T = 0 s(4i + 3)T -1.

Consequently, the output samples y(iT) of the translated signal are obtained from the input samples xi and xi according to the following schemes when e is chosen equal to 1: Input samples x(4iT) x(4i + 1)T x(4i + 2)T x(4i + 3)T x(4i + 4)T Input samples x(4iT) x(4i + 1)T x(4i + 2)T x(4i + 3)T x(4i + 4)T Output samples x(4iT) x(4i + 1)T-x(4i + 2)T-x(4i + 3)T x(4i + 4)T

The logic...