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Extra resources for Electronics for Hobbyists (Unit 7. Survey of Electronics Hobbies)
I f one simply adds consecutive pairs of samples together one has 9-bit data at half the sample rate. Adding consecutive pairs of the 9-bit samples together gives 10-bit data at 114 the 8-bit sample rate, and so on. ( a ) I f one continued on to get 16-bit data from the original 8-data sampled at 10,000 Hz, what would the data rate be for the 16-bit data? ( b ) Suppose we had a very fast device which samples data using only I -bit, 0 for negative and 1 for positive. How fast would the 1-bit A / D have to sample to produce 16-bit data at the standard digital audio rate of 44,100 samples per sec?
A compensated system response with separate “linear” scaling is depicted as H‘[z] in Eq. 15) below. “I] (2 -: ,)(I - q*) A,. 15) The partial fraction expansion coefficients A ( . ,B,, C,, and D,are seen in Eq. 16) for the all-pole part of the system response. 4, = B,. 16) D, = The compensated “linear” scaling shown in Eqs. 16) are seen as a compromise between matching the peak levels and maintaining consistent pole-zero frequencies. Another linear scaling technique seen in the literature applies to the z-plane mapped impulse response where A - , B,, C-, and D =are the unscaled mapped z-plane counterparts to the +plane coefficients given in Eq.
Eq. 1) is a discrete time Fourier transform (DTFT), the details of which will be explained in much greater detail in Chapter 5. If ~ “ 1 2 1is the output of it digital tiltcr driven by it broadband input signal s [ n ]containing every frequency of interest. the frequency response of the filter is found from system theory. 2) The impulse response of our digital filter is found most conveniently by computing the inverse discrete time Fourier transform (IDTFT) using the sum of the responses a t K frequencies of interest.