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Excerpted from Digital Receiver Handbook: Basics of Software Radio Sixth Edition, this series of articles from Pentek shows how digital receivers, the fundamental building block for software radio, can replace conventional analog heterodyne receiver designs, offering significant benefits in performance, density, and cost in the radio receiver circuit signal processing. See Part 1.
Digital Mixer
The next major component of the digital receiver chip is the mixer seen in Figure 9. The mixer actually consists of two digital multipliers. Digital input samples from the analog/digital (A/D) converter are mathematically multiplied by the digital sine and cosine samples from the local oscillator (LO).
9. The digital mixer consists of two digital multipliers.
Note that the input A/D data samples and the sine and cosine samples from the LO are being generated at the same rate, namely, once every A/D sample clock. Since the data rates into both inputs of the mixers are the A/D sampling rate fs, the multipliers also operate at that same rate and produce multiplied output product samples at fs.
The sine and cosine inputs from the LO create in-phase (I) and quadrature (Q) outputs that are important for maintaining phase information contained in the input signal. From a signal standpoint, the mixing produces a single-sideband complex translation of the real input.
Unlike analog mixers, which also generate many unwanted mixer products, the digital mixer is nearly ideal and produces only two outputs: the sum and difference
frequency signals.
Let's look at the "difference" mixer product in the frequency domain as shown in Figure 10. At the output of the mixer, the high frequency wideband signals in the A/D input have been translated down to DC with a shift or offset equal to the LO frequency.
10. Digital receiver mixer translation.
This is similar to the analog receiver mixer except that the analog receiver mixes the RF input down to an intermediate frequency (IF). In the digital receiver, the precision afforded by the digital signal processing allows us to mix right down to baseband (or 0 Hz). Overlapping mixer images, difficult to reduce with analog mixers, are strongly rejected by the accuracy of the sine and cosine LO samples and the mathematical precision of the multipliers in the digital mixer.
By tuning the local oscillator over its frequency range, any portion of the RF input signal can be translated down to DC. In effect, the wideband RF signal spectrum can be shifted around 0 Hz, left and right, simply by changing the LO frequency. The objective is to tune the LO to center the signal of interest around 0 Hz so that the low-pass filter that follows can pass only the signal of interest.
Decimating Low Pass Filter
Once the RF signal has been translated, it is now ready for filtering. The decimating low-pass filter accepts input samples from the mixer output at the full A/D sampling frequency fs. It utilizes digital signal processing to implement a finite impulse response (FIR) filter transfer function. The filter passes all signals from 0 Hz up to a programmable cutoff frequency or bandwidth, and rejects all signals above that cutoff frequency (Figure 11). This digital filter is a complex filter which processes both I and Q signals from the mixer. At the output you can select either I and Q (complex) values or just real values, depending on your system requirements.
11. Decimating Low Pass Filter.
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