How to pick correct filter for a given signal processing task?

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When it comes to selecting filters for signal processing, it's essential to understand that this task goes beyond mere simplicity. The key lies in meticulous attention to detail concerning specific performance specifications that must be met effectively.

The initial step in any design process is to thoroughly define all your requirements. Following that, create a detailed specification checklist!

• Considerations include cost versus quantity, R&D duration, spatial limitations, performance metrics, reliability, stability, and error budget tolerances.

• A solid grasp of DSP and filter theory is crucial, but equally important is the application theory or practical experience to make informed choices regarding Signal-to-Noise Ratio (SNR), Jitter, Group Delay Distortion, Phase Jitter, Bit Error Rate (BER), Inter Symbol Interference (ISI), Crossover Gain Flatness, Adjacent Channel Rejection, Image Rejection, and Local Oscillator (LO) Rejection among others.

  It may be that some professors’ lack of practical experience is reflected in how filter theory is taught.

This guide serves as a quick at-a-glance reference.

Filter Types by Physical Medium

{Passive, Analog Electronic, Digital, Interdigital, Surface Acoustic Wave (SAW), Ceramic/Xtal}

• Network Synthesis Filters:

  Butterworth Filter: Offers maximally flat amplitude response but exhibits significant group delay near its edges, leading to step overshoot.
  Chebyshev Filter: Known for its sharp skirts but entails a tradeoff with passband ripple.
  Cauer (Elliptic) Filter: Provides a steep skirt tradeoff suitable for Bandpass-Bandstop applications.
  Bessel Filter: Distinguished by its maximally flat group delay and linear phase characteristics.
  Gaussian Filter: Exhibits no overshoot for a step function input while maintaining minimal rise, close to Gaussian impulse approximation.
  Legendre Filter: A monotonic filter, unlike Chebyshev, with a slightly reduced initial steepness, also known as the "Optimal L".
  Raised Cosine Filter: Offers zero Inter-Symbol Interference (ISI) with various data patterns, minimizes jitter, but experiences tradeoffs with ringing at zero-crossings.
  Linkwitz-Riley Filter: Differentiates itself from other filters defined by -3dB, as its crossover Low Pass and High Pass combine for a flat sum at -6dB.

Impedance Filters

Common Filter Applications: Falstad Pass & Active, TI Filter Designer, and numerous others include:

RC Filter
RL Filter
LC Filter
RLC Filter

If you enjoy visualizing Pole-Zero plots or positioning peaks within the filter in unloaded scenarios, here’s an audio passive mid-band filter for your reference.

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Take note for future reference. The red line illustrated below represents the actual filter under load conditions, with the load resistor removed to unveil the poles that define the band edge. This example demonstrates how filters are shaped through a combination of staggered poles and zeros.

In this case, the source impedance is set to zero. Please note, this is not intended as a practical filter showcasing mH chokes with zero Direct Current Resistance (DCR), but rather serves as an illustration to emphasize the relationship between Q and pole placement, tapping into stronger visual memory retention.

Bessel Filters consistently present the lowest Q factor and group delay discrepancies while exhibiting the gentlest amplitude transitions at the breakpoint. Within each filter, individual poles and zeros are placed to optimize characteristics such as amplitude, delay, or phase slope, represented through various tradeoffs.

The mathematical characteristics are well-established, offering adjustable variables for ripple and potentially linear-phase error bandwidth beyond the -3dB breakpoint. The only distinction here is the chosen filter type (Butterworth, Chebyshev, Bessel).

The yellow line indicates a cursor-controlled 1 kHz on the plot for both Bode Plot and Pole-Zero Plot.

Each filter is set at a 1 kHz center frequency with a bandwidth of 3.78 kHz (this is an arbitrary mid-audio passband intended to eliminate bass and tweeter frequencies). The vertical scale measures 20 dB/grid.

This serves to illustrate the RLC equivalent circuits, steering clear of practical Active RC filter implementations. Future examples could include higher frequency filters, but that’s a topic for another time.

When dealing with high Q filters, take care to avoid potential aliasing errors (e.g., lower peak readings) that may arise whether using this simulation tool or conducting analysis through network or spectrum analyzers. Adjust video resolution or span where feasible.

Perhaps this overview isn’t as quick and straightforward as anticipated... ;) (* a nod to the informal spec notes from the 70s design era)

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