Unit 9 Digital Signal Processing,Passage A Basic Concepts of DSP Passage B Digital Signal Processors Passage C Comparison of DSP and ASP,Passage A Basic Concepts of DSP We dont speak in a digital signal. A digital signal is a language of 1s and 0s that can be processed by mathematics. We speak in real-world, analog signals. Analog signals are real world signals that we experience everyday-sound, light, temperature, and pressure. A digital signal is a numerical representation of the analog signal. It may be easier and more cost effective to process these signals in the digital world. In the real world, we can convert these signals into digital signals through the analog-to-digital converter, process the signals, and if needed, bring the signals back out to the analog world through the digital-to-analog converter.,1. The essentials of analog-to-digital and digital-to-analog conversion The first essential step in analog-to-digital (A/D) conversion (as shown in Figure 9.1) is to sample an analog signal. This step is performed by a sample and hold circuit, which samples at regular intervals called sampling intervals. The length of the sampling interval is the same as the sampling period, and the reciprocal of the sampling period is the sampling frequency fs. According to the Nyquist theorem, a signal with a maximum frequency of W Hz (called a band-limited signal) must be sampled at least 2W samples per second to ensure accurate recording. When this minimum is not respected, distortion called aliasing occurs. Aliasing causes high frequency signals to appear as lower frequency signals. To be sure aliasing will not occur, sampling is always preceded by low pass filtering. The low pass filter, called the anti-aliasing filter, removes all frequencies above half the selected sampling rate.,Figure 9.1 Analog-to-Digital Conversions,After a brief acquisition time, during which a sample is acquired, the sample and hold circuit holds the sample steady for the remainder of the sampling interval. This hold time is needed to allow time for an A/D converter to generate a digital code that best corresponds to the analog sample.,The A/D converter chooses a quantization level for each analog sample. An N-bit converter chooses among 2N possible quantization levels. The larger the number of levels, the smaller the quantization errors, calculated as the difference between the quantized level and the true sample level. Most quantization errors are limited in size to half a quantization step Q. The quantization step size is calculated as Q=R/2N, where R is the full scale range of the analog signal and N is the number of bits used by the converter. The strength of the signal compared to that of the quantization errors is measured by dynamic range and signal-to-noise ratio.,A digital signal is represented by a set of vertical lines with circles at the top to mark the quantization levels selected for each sample. The bit rate for an A/D converter is the Nfs, where fs is the sampling rate. Finally, each digital sample is assigned a digital code, which completes the A/D process. The result is a digital bit stream. It is this collection of digital codes that is processed in digital signal processing.,To summarize, A/D comprises anti-aliasing, sampling, quantization and digitization. Once digital signal processing is complete, digital-to-analog (D/A) conversion (as shown in Figure 9.2) must occur. This process begins by converting each digital code into an analog voltage that is proportional in size to the number represented by the code. This voltage is held steady through zero order hold until the next code is available, one sampling interval later. This creates a staircase-like signal that contains frequencies above W Hz. These signals are removed with a smoothing low pass filter, the last step in D/A conversion.,Figure 9.2 Digital-to-Analog Conversions,The images of each frequency f present in a sampled signal appear, through sampling, at the infinite number of frequencies kfsf Hz. When the sampling rate is lower than the required Nyquist rate, that is fs2W, images of high frequency signals erroneously appear in the baseband (or Nyquist range) due to aliasing. While this undersampling is normally avoided, it can be exploited. For example, signals whose frequencies are restricted to a narrow band of high frequencies can be sampled at a rate similar to twice the width of the band instead of twice the maximum frequency. All of the important signal characteristics can be deduced from the copy of the spectrum that appears in the baseband through sampling. Depending on the relationship between the signal frequencies and the sampling rate, spectral inversion may cause the shape of the spectrum in the baseband to be inverted from the true spectrum of the signal.1,2. Technologies for digital signal processing If a universal microprocessor solution existed with which every design could be realized, the electronics indu