Filtering

In what order must averaging and digital filtering be applied?

It doesn't really matter, as they are both linear operations. However, the files are smaller if averaging is done first

Why are digital filers beneficial?

they can increase SNR by lowering noise and remove unwanted frequencies from the data

What are potential drawbacks of digital filtering?

they can cause signal loss or distortion if they aren't used properly, changing the signal, resulting in temporal smearing, or "creating" a "signal" that doesn't really exist

Fourier's Theorem

states that nearly every wave can be expressed by superimposing single sinusoidal frequency waves

Fourier Synthesis

mathematical process of combining sine waves to create more complex periodic vibrations

Fourier analysis

A mathematical procedure by which any signal can be separated into component sine waves at different frequencies. Combining these sine waves will reproduce the original signal.

Frequency spectrum

a graph that shows the amplitudes of different frequencies present in a waveform

running average (boxcar filter)

an average consisting of a continuous window of averages of a certain number of data points

How does a waveform change when more points are added to a running average/boxcar filter?

it becomes more smooth as short fluxuations are eliminated, but temporal smearing also occurs and points at the end of the window are lost

Time frequency trade off

when frequencies are removed and waves are made more smooth and thus easier to analyze, timepoints at both ends of the window are also lost, resulting in temporal "smear" and loss of accuracy

What is a key difference between the points at which analog compared to digital filters can analyze?

digital filters can filter time using points before or after a given timepoint, while analog filters can only filter using points before a given timepoint

Pass band

the frequency region over which frequencies pass through the filter unchanged

stop band

the frequency region over which frequencies are attenuated

What is filter cutoff typically specified as?

the 50% amplitude cutoff, the frequency value at which 50% of a signal is passed (half amplitude or half power, -3dB)

cutoff slope

the steepness of the transition band of a filter

What are characteristics of a filter? (5)

1. analog or digital
2. low, high or band pass
3. cutoff frequency
4. cutoff slope
5. phase shifting vs zero phase (causal vs non-causal)

6 dB means...

50% drop in amplitude

3 dB means...

50% drop in power

Are high or low pass filters worse for signal distortion?

high pass, tend to have steeper transition bands

Butterworth Filter

Designed to have a gain which is maximally flat in the passband, have a capacitor, resistor, and inductor. Imitated by digital filters

Where is the cutoff for a filter normally put to prevent aliasing (analog low-pass filter)?

at 1/4 the Nyquist limit

What are guidelines for filtering? (3)

1. analog filtering should pass a broad range of frequencies to prevent phase shifting, but within the Nyquist limit
2. zero-phase (non-causal) filters only
3. only filter as much as needed