Degital Filters Flashcards
(16 cards)
What are the main differences between Digital and analogue filters
A digital filter is a numerical procedure selectiely extracts information from the input into an output digital signal. An analogue filter can be provided inanaltical form but can also be designed in the form of electrical circuitary.
What do we use filters for?
To extract information from a signal in a certain frequency range. To either be used to analyse the signal in this range or to remove content of a time sequence e.g. noise or artefacts. We can also chose to enhance the signal at certain frequencies like edge enhancing medical images.
What are the 3 main domains in which are the transfer functions from a filter normally presented
Time domain impulse response, Laplace (analogue filter), Z-transofrm (digital filter). All of these free transforms are used or linear time invariant systems
What are the assumptions of an ideal filter which cannot be achieved with a real filter
No ripples in the stop band, no overshoot in the pass band, zero transition band
Definition of decibel, why do we use this when decribing a digital filter
A logarithmic unit that indicatesthe ratio of a physical quantity (usualy power or intensity) relative to a specified or implied reference level. 10dB is a change by 10, 3dB is a change by 2.
Explain the process of FIR filter design using a window funciton
- Define a function in the frequency domain with desired frequency response
- Perform inverse fourier transform to get H(n) in time domain
- Perform convolution in time domain with a corresponding window function to get finite length e.g. (fil(n) = H(n)*hamming(n)
- Creating a signal which can be convolved with a signal in the time domain x(n)*fil(n) or can be multiplied in frequency domain.
what is a bilinear transform used for
Used when designing IIR filters. First deign an analogue filter then convert it into a digital filter using a bilinear transform
Explain the basic steps in design of a digital filter from analogue filters
Use low pass filter to define H(s)
- create OMegai = tan(wi/2)
- replace s in transfer function using H(s) in table
- Apply bilinear transform
What are the common characteristics of an analogue and derived digital filter which don’t have the same number of poles and zeros.
They have the same magnitude and phase characteristics. it is easier to create a desired amplitude and phase characteristic of an analogue filter than of a digital filter because we can present it in analytical form. We use bilinear transforms to choose desired magnitude and phase characteristic and then create a notch filter.
write and explain the z transform and inverse z transform
define DFT
Z-transform presents a sequince x(n) as a sum of SCALED sinusoid functions (r can vary therefore more general)
DFT presents a sequence x(n) as a sum of sinusoid functions.
Which is more general z or DTFT
Z is more general as it may exist even when DTFT does not. Both transforms assume a system in linear and time invariant and Z only exists when z transform is converging.
DFT only exists when r = 1. z transform also exists here.
We use DFT to present frequency content of a time series, we can present is as a weighted sum of a signal frequency exponential function only on a unit circle (when r = 1 in z transform.
What are the assumptions a z transform makes of a system
The system is time invariant and linear
Define convolution
When signals are multiplied in the z domain
Explain the relation to energy spectral density and Power spectral density
Energy S.D. Shows how the energy of a signal is distributed over frequency
PSD is obtained when ESD is decided by a finite time period in which a signal was measured
Explain the Welsh periodogram for calculating PSD
Wlesh periodogram is a method which decides a time sequence into smaller time domains and then presents PSD of the whole time sequence as an average of these short sequenced PSDs. The advantage of this is over calculating PSD over the whole signal is that averaging smooths PSD so the, location of peaks indicating frequencies which bear the most of energy become much clearer.
What are the differences between equiriple (hamming) window design and a kaiser (hand) window design
equiripple filters are designed to provide equal attenuation in a stopband across all frequencies. Therefore if we can still notice some frequency in the stopband, we will not get a wrong impression that a
frequency content on lower frequencies in the stopband is of a higher magnitude that the one at higher frequincies
The kaiser window will attenuate higher frequencies in the stop band more, however has a longer transition band
