ADVANCED DIGITAL SYSTEMS

Advanced Digital Systems



Advanced Digital Systems

Introduction

Digital filtering is one of the most powerful tools of DSP. Apart from the obvious advantages of virtually eliminating errors in the filter associated with passive component fluctuations over time and temperature, op amp drift (active filters), etc., digital filters are capable of performance specifications that would, at best, be extremely difficult, if not impossible, to achieve with an analog implementation. In addition, the characteristics of a digital filter can be easily changed under software control. Therefore, they are widely used in adaptive filtering applications in communications such as echo cancellation in modems, noise cancellation, and speech recognition.

The actual procedure for designing digital filters has the same fundamental elements as that for analog filters. First, the desired filter responses are characterized, and the filter parameters are then calculated. Characteristics such as amplitude and phase response are derived in the same way. The key difference between analog and digital filters is that instead of calculating resistor, capacitor, and inductor values for an analog filter, coefficient values are calculated for a digital filter. So for the digital filter, numbers replace the physical resistor and capacitor components of the analog filter. These numbers reside in a memory as filter coefficients and are used with the sampled data values from the ADC to perform the filter calculations. The real-time digital filter, because it is a discrete time function, works with digitized data as opposed to a continuous waveform, and a new data point is acquired each sampling period. Because of this discrete nature, data samples are referenced as numbers such as sample 1, sample 2, sample 3, etc. Figure below shows a low frequency signal containing higher frequency noise which must be filtered out. This waveform must be digitized with an ADC to produce samples x(n). These data values are fed to the digital filter, which in this case is a lowpass filter. The output data samples, y(n), are used to reconstruct an analog waveform using a low glitch DAC. Digital filters, however, are not the answer to all signal processing filtering requirements. In order to maintain real-time operation, the DSP processor must be able to execute all the steps in the filter routine within one sampling clock period,1/fs. A fast general purpose fixed-point DSP such as the ADSP-2189M at 75MIPS can execute a complete filter tap multiply-accumulate instruction in 13.3ns. The ADSP-2189M requires N+5 instructions for an N-tap filter. For a 100-tap filter, the total execution time is approximately 1.4µs. This corresponds to a maximum possible sampling frequency of 714 kHz, thereby limiting the upper signal bandwidth to a few hundred kHz (Punskaya E., 2008),.

Figure 1 Digital filters, (Kester W., n.d.)

Design justification

Simple ?lters

There are two methods for smoothing a sequence of numbers in order to approximate a low-pass ?lter: the polynomial ?t, as just described, and the moving average. In the ?rst case, the approximation to a LPF can be improved by using a higher-degree polynomial: for example, instead of using a quadratic as in ...