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Circuit Surgery Regular clinic by Ian Bell Topics in digital signal processing – windowed sinc filters W e are looking at various topics related to digital signal processing (DSP). DSP covers a wide range of electronics applications where signals are manipulated, analysed, generated, stored or displayed as digital data but originate from and/or are converted to real-world signals for interaction with humans or other parts of the physical world. Fig.1 shows the key elements of a generic DSP system with a signal path from an analog input via digital processing to an analog output. This does not necessarily represent every DSP system (not all have all the parts shown), but it serves as a reference for the various subsystems we will consider. Last month, we started looking at the windowed sinc filter, which is a widely used type of digital filter. We discussed the “sinc” aspect of the filter’s name, which refers to the fact that its impulse response takes the form of the mathematical sinc function. The impulse response is the output obtained from a system when the input is an impulse. For a sampled data system, this is a single input sample of value 1 at time zero, with an input of zero at all other times. For a Finite Impulse Response (FIR) filter (Fig.2), the coefficients (the ai values in Fig.2) are equal to the impulse response of the filter. So, if we know the impulse response of the desired filter, we have the coefficient values required to implement it. As discussed last month, we can obtain the impulse response of a filter by performing an inverse Fourier Transform on the required filter frequency response. The result for an ideal low-pass filter (a ‘brick wall’ filter) is that the impulse response is a sinc function, hence the Analog In Antialiasing filter Sample and hold importance of the sinc function in filter implementation. We showed how to use a spreadsheet to calculate an example set of low-pass filter coefficients, normalising the DC gain to one. Filter & simulation improvements The sinc function has non-zero values over an infinite range, so a perfect filter would require an infinite number of coefficients. That is obviously not practical, so last month we simply used the relevant sinc function values up to a specific number of coefficients. Truncating the coefficients like this does not necessarily produce the best results, which is where the “windowing” part of the filter name comes in. Before getting into that, though, we will continue our discussion on using LTspice to simulate these filters. In previous articles, we used LTspice to implement digital filter maths for obtaining frequency response plots or transient simulations of just the filter, or the filter together with other subsystems such as sampling and reconstruction filters (see Fig.1). Our approach uses LTspice behavioural voltage sources to implement the delay, multiply and add operations shown in the filter structure of Fig.2. Last month, we showed an FIR filter example with 25 coefficients, which required drawing 24 behavioural sources on the schematic to implement the delays. As a reminder, part of the schematic from last month is shown in Fig.3. This includes just five of the 24 delay sources, and the input signal source is also not shown. We may need to investigate filters with many more coefficients, or circuits with multiple filters, but in doing so, it becomes increasing cumbersome to draw Digital ADC Digital processing Analog DAC Fig.1: a generic digital signal processing (DSP) system structure. 46 Reconstruction filter the schematic. We need a better way to create large filters. SPICE netlists Although we usually draw schematics when using LTspice, the simulator actually uses a text description of the circuit, called a netlist, which is generated from the schematic drawing. SPICE simulators go back to the 1970s, before the days of high-resolution graphical user interfaces, so text has always been the format for circuit input. The libraries of component models provided with LTspice or via downloads are also primarily text-based netlists or model statements. You can view the netlist of a schematic from the main menu using View → SPICE Netlist. For the circuit from last month, the netlist will be similar to that shown in Fig.4, although the lines may be in a different order. Fig.4 only shows the first and last three behavioural sources used to implement the delays. Still, it should be clear that the regular structure of the circuit leads to a repetitive form for the code relating to these sources in the netlist. This means it is reasonably easy to create the netlist of a larger filter without a0 x(n) × Σ y(n) a1 Δt x(n–1) × a1x(n–1) Σ a2 Δt x(n–2) × a2x(n–2) Σ aN–1 Δt Out a0x(n) Memory x(n–N–1) × aNx(n–N–1) Processing Fig.2: the structure of a finite impulse response (FIR) filter. Practical Electronics | March | 2025