tailieunhanh - Understanding digital signal processing - Chapter 10

Tài liệu tham khảo giáo trình tìm hiểu xử lý tín hiệu số bằng tiếng anh ( Understanding digital signal processing ) Chương 10. Thủ thuật xử lý tín hiệu kỹ thuật số | CHAPTER TEN Digital Signal Processing Tricks As we study the literature of digital signal processing we ll encounter some creative techniques that professionals use to make their algorithms more efficient. These techniques are straightforward examples of the philosophy don t work hard work smart and studying them will give US a deeper understanding of the underlying mathematical subtleties of digital signal processing. In this chapter we present a collection of these clever tricks of the trade and explore several of them in detail because doing so reinforces some of the lessons we ve learned in previous chapters. Frequency Translation without Multiplication Frequency translation is often called for in digital signal processing algorithms. A filtering scheme called transmultiplexing using the FFT to efficiently implement a bank of bandpass filters requires spectral shifting by hah the sample rate or s 2 l . Inverting bandpass sampled spectra and converting low-pass FIR filters to highpass filters both call for frequency translation by half the sample rate. Conventional quadrature bandpass sampling uses spectral translation by one quarter of the sample rate or fs 4 to reduce unnecessary computations 2 3 There are a couple of tricks used to perform discrete frequency translation or mixing by s 2 and s 4 without actually having to perform any multiplications. Let s take a look at these mixing schemes in detail. First we ll consider a slick technique for frequency translating an input sequence by fs 2 by merely multiplying that sequence by -1 or -1 -1 1 -1 2 I 3 etc. Better yet this requires only changing the sign of every other input sample value because -1 1 -1 1 -1 etc. This process may seem a bit mysterious at first but it can be explained in a straightforward way if we review Figure 10-1. The figure shows us that 385 386 Digital signal Processing Tricks Figure 10-1 Mixing sequence comprising -l n 1 -1 1 -1 etc. multiplying a time-domain signal sequence by the