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What is convolution?

A mathmatical principle that takes two vectors (the input signal) and the impulse response to give a third vector (the filtered signal)


What is FFT?

Fast fourier transformation - continuous in time and ampltiude measurements


What is a condition of the FFT?

The number of samples must be a power of 2.


How many unique components are there in the DFT?



What is the smallest Hz that can be resolved in the fourier spectrum?

The fundamental Hz that is independant of the sampling Hz but dependant on the sampling period.


For real the sampling period is:

The period over which the sample was recorded.


What does increasing the sampling Hz do to the fourier spectrum?

It does not alter the number of spectral components, there are more components in the Hz domain but these have an amplitude of zero


How do we interpolate in the Hz domain?

Padding with zeros increase the number of samples for the inverse fourier transformation back into the time domain and is therefore equivalent to interpolation in the time domain

This is because interpolation is the process of estimating the values of other samples based on the preexisting samples to smooth out the curve.


What is the relationship between the number of points in the input data and the Hz spectrum?

Real and imaginary spectrums have the same number of points as the input data


Describe the Hz at the end, middle and beginning of the real and imaginary spectra;

End = Sampling Hz
Middle = (N-1)/2)
Beginning = 1/S(t)


What alters the Hz domain resolution?

Increasing the data length increases the resolution of the Hz domain but doesnt alter the underlying distribution


What happens if you increase the sampling Hz to the fourier spectrum?

It increases the number of hz components but some of these have values of zeros like zero padding, it does not alter the spectral Hz.


How is aliasing prevented when nyquist criterion is used to select the sampling Hz?

A low bass band filter is used with a cut off just above the nyquist Hz therefore preventing high Hz noise alaising low frequencies.


What enhances the resolution of the digital signal?

Increasing the number of bits in the AD converter.


What does increasing the number of points in the smoothing average do to the noise and magnitude and roll off?

- The noise is reduced as the weighted co-efficients generate an average using the surrounding data.

- The magnitude of a point is reduced is also reduced with a larger n point filter because more smaller values can be included in the average.

- The roll off will steepen as the increased number of points will create a more rapid change in values.


How are the impulse response and frequency response related?

The impulse response, h(t)is the inverse Fourier transform of the filter frequency response, H(f)


How can phase shift be introduced in a filter?

Non-recursive filters can introduce a phase delay (time shift) between the input and output but when the convolution is symmetric no phase shift is introduced.


Why are filter non-recursive?

non-recursive filter because there is no feedback of the output to be used as an input

•Also called a Finite Impulse Response (FIR) filter because the impulse response settles to zero within a finite length of time


How is a performance of a filter assessed?

•The performance of a filter is best assessed in the frequency domain

•Frequency response is the Fourier transform, H(f), of the impulse response, h(t)


What causes filters to ripple?

Filter order is n-1. Higher the order the sharper the transition but also more prone to ripple effect – i.e. leakage


What generates a higher cut off Hz of a filter?

Fc(cut-off frequency) is adjusted by time scaling the impulse response-> Fewer terms gives a higher cut-off frequency


What are the types of FIR filters and not FIR?

FIR = n point moving average

Not FIT = blackman and brick wall fitler as impulse response extends infinitely in the time domain`


Why must a filter be symmetrical in the Hz domain?

TO preserve the symmetry of the DFT or in this case inverse FT.