DSP Tricks: Frequency Translation Using Decimation - Embedded.com

DSP Tricks: Frequency Translation Using Decimation

We can frequency translate a real bandpass signal toward zero Hz, converting it to a lowpass signal, without the need for mixing multipliers using decimation by an integer factor D as shown in Figure 13-75(a) , below.

Figure 13-75. Real bandpass signal translation using decimation by D.

If the bandpass filter provides an output signal of bandwidth B Hz, located as shown in Figure 13-75(b) and Figure 13-75(d) where k is a positive integer, decimation by D will yield lowpass signals whose spectra are shown in Figure 13-75(c) and Figure 13-75(e) depending on whether integer k is odd or even.

Please notice the inverted spectra in Figure 13-75(e).

To avoid decimated output aliasing errors, we must satisfy the Nyquist criterion and ensure that xBP (n)'s bandwidth B is not greater than fs /2D.

Usedwith the permission of the publisher, Prentice Hall, this on-goingseries of articles on Embedded.com is based on copyrighted materialfrom “UnderstandingDigital Signal Processing, Second Edition” by Richard G. Lyons. Thebook can be purchased on line.

Richard Lyons is a consultingsystems engineer and lecturer with Besser Associates. As alecturer with Besser and an instructor for the University of CaliforniaSanta Cruz Extension, Lyons has delivered digitasl signal processingseminars and training course at technical conferences as well atcompanies such as Motorola, Freescale, Lockheed Martin, TexasInstruments, Conexant, Northrop Grumman, Lucent, Nokia, Qualcomm,Honeywell, National Semiconductor, General Dynamics and Infinion.

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