Filter design raspberry pi2/18/2024 ![]() You might be wondering why we wouldn’t just set the transition width as small as possible. The Red line demonstrates the result of a realistic filter, which has some ripple and a certain transition width. ![]() In the diagram below, the green line represents the ideal response for transitioning between a passband and stopband, which essentially has a transition width of zero. Transition width, also measured in Hz, instructs the filter how quickly it has to go between the passband and stopband since an instant transition is impossible. In addition to cutoff frequency, the other main parameter of our low-pass filter is called the “transition width”. It’s now below where the noise floor was! We also removed most of the noise that existed in the stopband. Even though we can still see the interfering signal centered at 10 kHz, we have severely decreased the power of that signal. This filtered signal will look confusing until you recall that our noise floor was at the green line around -65 dB. Our cutoff frequencies will look something like this (the passband is the area in between):Īfter creating and applying the filter with a cutoff freq of 3 kHz, we now have: I.e., it’s symmetrical around DC (later on you will see why). However, the way most low-pass filters work, the negative frequency boundary will be -3 kHz as well. In this example, 3 kHz seems like a good value: Cutoff frequency will always be in units of Hz. corner frequency), which will determine when the passband transitions to stopband. We must choose a “cutoff frequency” (a.k.a. Here is what we might receive:īecause our signal is already centered at DC (0 Hz), we know we want a low-pass filter. We will have to keep track of which frequency we told the SDR to tune to. Remember that we tell our SDR which frequency to tune to, but the samples that the SDR captures are at baseband, meaning the signal will display as centered around 0 Hz. To learn how filters are used, let’s look an an example where we tune our SDR to a frequency of an existing signal, and we want to isolate it from other signals. ![]() Here is an example of a set of filter taps, which define one filter: We often use as the symbol for filter taps. ![]() We call this array of floats “filter taps”. For filters symmetrical in the frequency domain, these floats will be real (versus complex), and there tends to be an odd number of them. Filter Representation ¶įor most filters we will see (known as FIR, or Finite Impulse Response, type filters), we can represent the filter itself with a single array of floats. LPF allows us to filter out everything “around” our signal, removing excess noise and other signals. The most common type by far is the low-pass filter (LPF) because we often represent signals at baseband. For a high-pass and band-pass filter, 0 Hz will always be in the stopband.ĭo not confuse these filtering types with filter algorithmic implementation (e.g., IIR vs FIR). In the case of the low-pass filter, it passes low frequencies and stops high frequencies, so 0 Hz will always be in the passband. The range of frequencies a filter lets through is known as the “passband”, and “stopband” refers to what is blocked. In DSP, where the input and output are signals, a filter has one input signal and one output signal:Įach filter permits certain frequencies to remain from a signal while blocking other frequencies. The following image juxtaposes a schematic of an analog filter circuit with a flowchart representation of a digital filtering algorithm. However, it’s important to know that a lot of filters will be analog, like those in our SDRs placed before the analog-to-digital converter (ADC) on the receive side. You may think we only care about digital filters this textbook explores DSP, after all. There are certainly other uses for filters, but this chapter is meant to introduce the concept rather than explain all the ways filtering can happen. Restoration of signals that have been distorted in some way (e.g., an audio equalizer is a filter) Removal of excess noise after receiving a signal Separation of signals that have been combined (e.g., extracting the signal you want) You might use a filter every morning to make your coffee, which filters out solids from liquid. For example, image processing makes heavy use of 2D filters, where the input and output are images. ![]() Filter Basics ¶įilters are used in many disciplines. We finish with an introduction to pulse shaping, which we further explore in the Pulse Shaping chapter. We cover types of filters (FIR/IIR and low-pass/high-pass/band-pass/band-stop), how filters are represented digitally, and how they are designed. In this chapter we learn about digital filters using Python. ![]()
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