This picture below is part of lecture note from MIT 6.334 Power Electronics course. The link to the lecture is also given below.
I am a bit confused about the conditions for moving average of a product approximation.
The two conditions are as follows:
1) small ripple
2) slow variance
For small ripple, I think that is to make it look like a constant. However, why do we need "slow variation"?
Let's say the signal x = X + A*sin(2*pi*f*t) including a constant DC component X and a ripple with frequency f, amplitude A.
1. small ripple: the amplitude A is much smaller than X or (A
Dear Huan,
The moving average filter acts as low pass filter in the continuous time domain, having a sinc frequency transfer function. I used for many times exponential moving average filter for ADC sampled data filtering: y(t) = (1-a)*y(t-1) + a*x(t). x(t) is the new data, a is filter factor. This is an low pass filter with Tf = Ts/(ln(1/(1-a)) time constant. Tsmin>1/2Bf (Bf = signal frequency bandwith) from Nyquist theorem. So, you have to choose the ADC sampling time less the Tsmin and the filtering factor close to signal frequency bandwidth.
The preconditions have to do with mathematics - less with the process of averaging itself:
avg(x(t)) * avg(y(t)) ≠ avg(x(t)) * avg(y(t)) this is the general equation
Only if at least x'(t) or y'(t) has low ripple and variation (meaning one of the terms is near-constant), the average of the product is approximately the same as the product of the individual averages.
(Consider averaging as a synonym for 'integration': all rules and considerations about integration apply for averaging similarly.)
Hope this helps
Dear Huan,
Dear Colleagues,
The moving average filter is thought to attenuate the switching ripples at the output of the inverter. It passes the slow variations of the output voltage. This is okay since it is a low pass filter.
i would like to quote the hand outs brought by Huan. The author wrote:
The local average: tracks the low frequency variations suppress switching ripples.
Take care of tracks the low frequency partitions!!!!!!!!
So the summation time must sufficiently small to allow such slow variations to pass. This condition fix the integration time or the cut off frequency of the filter.
it is only the higher frequency components that must be eliminated, no doubt.
Best wishes
I look at averaging as a form of filtering. Filters have a frequency response, and the effect of averaging will depend on this. Generally low frequency filters obtained by averaging over large N will provide smoothening effect, and unfortunately also have a transient response which needs to be considered. Non linear filters can provide a compromise.
A "ripple" by itself is not specifying the frequency that needs to be rejected. A "ripple" may be a low amplitude variation of the dc. But it can be at 1hz, 100hz or even 0.1 hz. The performance improvement obtained will largely depend on the frequency of variation of the signal, also. Moving average filters which are also adaptive can help reduce the variations but will also have time response which may be objectionable in some cases.. One method of filtering which remove the interference altogether is based on NMR of ADC's wherein the signal is integrated over full cycle of the interference. If the disturbance is at a specific frequency this can help.
In one form of a non linear filter, the output is set to be equal to input to start with. This reduces the build up time ... I have used this in a cabin pressure control system wherein pressure is maintained within limits as aircraft altitude rises.
Averaging is as a word which can mean many things.. One should qualify this word with many adjectives to indicate what the averaging does. e.g., What is the average of the mains voltage? This could be hourly average, daily average or even monthly average?? !! With computing capability one can make filters do many things... they can enhance, can reject, can suppress variations to desired level, at the cost of time.
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