Lec1 : Introduction to filters Flashcards
Powerline interference as an example of why filtering is required?
- Powerline interference (or mains) is frustratingly common! In a perfect world we could remove it completely
- Consider this example, a 500 Hz signal contaminated with 50 Hz interference
How can we define a filter system?
A filter system can be defined by a transfer function
H(ejω)
How is the transfer function used for the following analog circuit?
How do actual filters compare to ideal filters?
Primary differences between actual and ideal filters?
Also seen as the compromises made when making real filters
- Passband ripple
- Stopband Ripple
- Roll off(transition bandwidth)
- phase response
Equation for Gain(dB)?
Gain(dB) = 20log(Vout/Vin)
How can the stopband, passband, bandwidth, be shown on a filter output graph?
(frequency response)
The graph showing the phase response of a filter?
The purpose of the phase reponce?
- The phase response tells us how much each frequency component is shifted by in time.
- We consider a filter to have a cut-off frequency fc at the point where the amplitude has reduced to -3 dB that of the passband.
Uses of the running average filter?
The is commonly used to “smooth” data such as stock market values, it is also the filter that excel uses to smooth plots
A non-casual filter?
- If we have stored data then we can use past and future values – this is a non-causal filter
A casual filter?
A real time system can only use present and past values – this is a causal filter
How is filtering a continuous process?
- It is important to realise that the filtering process is continuous, in the sense that the coefficients are static but as time passes by the values of x[n] will be constantly changing depending on the input waveform
Convolution?
The concept of a set of static coefficients being applied to a sliding window is known as convolution, each input is multiplied by a coefficient and summed
The convolution equation
The difference equation for a three point running avergae filter?
Filter coefficients overview?
Low Pass Filter frequency response?
High Pass filter frequency response?
Band pass filter frequency repsonce?
Band Stop filter frequency responce?
Low band pass filter frequency responce?
Band high pass filter response?
Low band high pass filter response?
