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Hello Folks At the moment I am trying to design a one pole simple IIR digital filter to simulate thermal heating and cooling delay effect with simple equations like 1 - e^(-t/T), where T is a known time constant. I think an one pole IIR filter will do it: Y[n] = alpha/[1- (1-alpha)Z^(-1)] can simulate the delay effect when alpha < 1. But I am quite pullzing how the alpha will be determined. i'd appreciate if you shed some light on this. Best regards, Gordon Ao |
Exponenital Filter design
Started by ●January 24, 2005
Reply by ●January 24, 20052005-01-24
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Gordon- > At the moment I am trying to design a one pole simple IIR digital > filter to simulate thermal heating and cooling delay effect with > simple equations like 1 - e^(-t/T), where T is a known time > constant. I think an one pole IIR filter will do it: Y[n] = alpha/[1- > (1-alpha)Z^(-1)] can simulate the delay effect when alpha < 1. But I > am quite pullzing how the alpha will be determined. i'd appreciate > if you shed some light on this. The time domain implementation (difference equation) for your LPF is: y[n] = (alpha)x[n] + (1-alpha)y[n-1] If you choose alpha small then you can see the filter is "slow" -- it responds slowly to new input. If you give it an impulse response, then the rate of decay is 1/(1-alpha). From that you can pick alpha to be the time constant you need -- how many samples it should take for the decay to reach your desired minimum value. -Jeff |
Reply by ●January 25, 20052005-01-25
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Gordon, For the low-pass filter below, the alpha can be shown to be equal to alpha = 1/(1+(Sampling_Interval/Time_Constant)). Since you know the time constant and sampling interval, you can find out this quantity. It is approximately inverse of Number Samples in the time-constant when the time-constant is >> 1. Regards arun -----Original Message----- From: Jeff Brower [mailto:] Sent: Monday, January 24, 2005 9:48 PM To: Gordon Ao Cc: Subject: Re: [matlab] Exponenital Filter design Gordon- > At the moment I am trying to design a one pole simple IIR digital > filter to simulate thermal heating and cooling delay effect with > simple equations like 1 - e^(-t/T), where T is a known time > constant. I think an one pole IIR filter will do it: Y[n] = alpha/[1- > (1-alpha)Z^(-1)] can simulate the delay effect when alpha < 1. But I > am quite pullzing how the alpha will be determined. i'd appreciate > if you shed some light on this. The time domain implementation (difference equation) for your LPF is: y[n] = (alpha)x[n] + (1-alpha)y[n-1] If you choose alpha small then you can see the filter is "slow" -- it responds slowly to new input. If you give it an impulse response, then the rate of decay is 1/(1-alpha). From that you can pick alpha to be the time constant you need -- how many samples it should take for the decay to reach your desired minimum value. -Jeff |
Reply by ●January 25, 20052005-01-25
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A correction: alpha = 1/(1+(Time_Constant/Sampling_Interval)). Sorry for the inconvenience. Regards arun -----Original Message----- From: arun d naik (WT01 - EMBEDDED & PRODUCT ENGINEERING SOLUTIONS) Sent: Tuesday, January 25, 2005 5:08 PM To: 'Jeff Brower'; Gordon Ao Cc: Subject: RE: [matlab] Exponenital Filter design Gordon, For the low-pass filter below, the alpha can be shown to be equal to alpha = 1/(1+(Sampling_Interval/Time_Constant)). Since you know the time constant and sampling interval, you can find out this quantity. It is approximately inverse of Number Samples in the time-constant when the time-constant is >> 1. Regards arun -----Original Message----- From: Jeff Brower [mailto:] Sent: Monday, January 24, 2005 9:48 PM To: Gordon Ao Cc: Subject: Re: [matlab] Exponenital Filter design Gordon- > At the moment I am trying to design a one pole simple IIR digital > filter to simulate thermal heating and cooling delay effect with > simple equations like 1 - e^(-t/T), where T is a known time > constant. I think an one pole IIR filter will do it: Y[n] = alpha/[1- > (1-alpha)Z^(-1)] can simulate the delay effect when alpha < 1. But I > am quite pullzing how the alpha will be determined. i'd appreciate > if you shed some light on this. The time domain implementation (difference equation) for your LPF is: y[n] = (alpha)x[n] + (1-alpha)y[n-1] If you choose alpha small then you can see the filter is "slow" -- it responds slowly to new input. If you give it an impulse response, then the rate of decay is 1/(1-alpha). From that you can pick alpha to be the time constant you need -- how many samples it should take for the decay to reach your desired minimum value. -Jeff |
Reply by ●January 25, 20052005-01-25
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Gordon- Here is an e-mail I got from Jon Lark at L-3 Com (AS Div) that might be helpful: > If you choose Alpha = Ts/Tau > Where > Ts is the sampling interval > Tau is the desired Time constant Then the step response will > closely match the step response of the corresponding analog filter > with the transfer function > G(s) = 1/(Tau*s + 1) This appears similar to what Arun Naik suggested. -Jeff -------- Original Message -------- Subject: Re: [matlab] Exponenital Filter design Date: Mon, 24 Jan 2005 10:17:48 -0600 From: Jeff Brower <> Organization: Signalogic, Inc To: Gordon Ao <> CC: Gordon- > At the moment I am trying to design a one pole simple IIR digital > filter to simulate thermal heating and cooling delay effect with > simple equations like 1 - e^(-t/T), where T is a known time > constant. I think an one pole IIR filter will do it: Y[n] = alpha/[1- > (1-alpha)Z^(-1)] can simulate the delay effect when alpha < 1. But I > am quite pullzing how the alpha will be determined. i'd appreciate > if you shed some light on this. The time domain implementation (difference equation) for your LPF is: y[n] = (alpha)x[n] + (1-alpha)y[n-1] If you choose alpha small then you can see the filter is "slow" -- it responds slowly to new input. If you give it an impulse response, then the rate of decay is 1/(1-alpha). From that you can pick alpha to be the time constant you need -- how many samples it should take for the decay to reach your desired minimum value. -Jeff |
Reply by ●January 28, 20052005-01-28
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Arun and Jeff, Many thanks for the great insight and reply. I will try to experiment it shortly and let you know what I get. Sorry I did not see your message sooner. cheers, Gordon --- wrote: > > Gordon, > For the low-pass filter below, the alpha can be > shown to be equal to > alpha = 1/(1+(Sampling_Interval/Time_Constant)). > Since you know the time > constant and sampling interval, you can find out > this quantity. It is > approximately inverse of Number Samples in the > time-constant when the > time-constant is >> 1. > Regards > arun > > -----Original Message----- > From: Jeff Brower [mailto:] > Sent: Monday, January 24, 2005 9:48 PM > To: Gordon Ao > Cc: > Subject: Re: [matlab] Exponenital Filter design > Gordon- > > > At the moment I am trying to design a one pole > simple IIR digital > > filter to simulate thermal heating and cooling > delay effect with > > simple equations like 1 - e^(-t/T), where T is a > known time > > constant. I think an one pole IIR filter will do > it: Y[n] = alpha/[1- > > (1-alpha)Z^(-1)] can simulate the delay effect > when alpha < 1. But I > > am quite pullzing how the alpha will be > determined. i'd appreciate > > if you shed some light on this. > > The time domain implementation (difference equation) > for your LPF is: > > y[n] = (alpha)x[n] + (1-alpha)y[n-1] > > If you choose alpha small then you can see the > filter is "slow" -- it > responds slowly > to new input. If you give it an impulse response, > then the rate of > decay is > 1/(1-alpha). From that you can pick alpha to be the > time constant you > need -- how > many samples it should take for the decay to reach > your desired minimum > value. > > -Jeff > ------------------------ Yahoo! Groups Sponsor > Confidentiality Notice > The information contained in this electronic > message and any attachments to this message are > intended for the exclusive use of the addressee(s) > and may contain confidential or privileged > information. > If you are not the intended recipient, please notify > the sender at Wipro or > immediately > and destroy all copies of this message and any > attachments. > ===== ___________________________________________________________ ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com |
