DSP Tricks: Frequency Translation Using Decimation

Richard G. Lyons

August 29, 2008

Richard G. Lyons

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 x_BP(n)'s bandwidth B is not greater than f_s/2D.

Used with the permission of the publisher, Prentice Hall, this on-going series of articles on Embedded.com is based on copyrighted material from "Understanding Digital Signal Processing, Second Edition" by Richard G. Lyons. The book can be purchased on line.

Richard Lyons is a consulting systems engineer and lecturer with Besser Associates. As a lecturer with Besser and an instructor for the University of California Santa Cruz Extension, Lyons has delivered digitasl signal processing seminars and training course at technical conferences as well at companies such as Motorola, Freescale, Lockheed Martin, Texas Instruments, Conexant, Northrop Grumman, Lucent, Nokia, Qualcomm, Honeywell, National Semiconductor, General Dynamics and Infinion.