I need to design an FIR high-pass filter to attenuate frequencies from 20Hz and below. I need the order to be around 8 since I will be implementing the filter on a microcontroller. When using MATLAB FDAtool, there are only Fpass and Fstop as the input parameters. Is there an option to input Fc only (since Fpass and Fstop are not known)? or is there a way to determine Fpass and Fstop from the order number and the cut-off frequency?
It may be a bit naive to think about implementing a filter and consider only the cut-off frequency. In reality, there are several parameters to a filter which must be considered. An ideal filter that only has cut-off frequency would be infinite order, and therefore impossible to implement.
Look at this image to get an idea of the different considerations present in real filter design.
But I'll go ahead and try to read the tea leaves, here:
Select highpass. You will probably want to choose 20Hz as the value for Fstop, though you should be aware that frequencies slightly above this value will also be slightly (but less-so) attenuated. Fpass is the frequency at which the attenuation effectively stops.
Your pass and stop bands will have an amplitude ripple that you will also probably want to specify. Tightening these will increase the order of your filter.
I am trying to design a filter whose magnitude is the same as that of a given signal. The given signal is wind turbine noise, so it has significant low-frequency content. After designing the filter, I want to filter white Gaussian noise so as to create a model of wind turbine noise. The two signals, that is the original and the filtered noise should sound similar.
I am using arbitrary magnitude filter design in Matlab for that (FIR, Order: 900, Single rate, 1-band, response specified by amplitudes, Sample rate 44100 Hz, Design method: firls). The problem is that, although I design the filter using the values from the original signal's magnitude, the filter magnitude fails to follow the magnitude at higher frequencies. Could you please help me with that?
Thank you!
I use Matlab to calculate the fft result of a time series data. The signal has an unknown fundamental frequency (~80 MHz in this case), together with several high order harmonics (1-20th order). However, due to finite sampling frequency (500 MHz in this case), I always get the mixing frequencies from high order frequency (7-20), e.g. 7th with a peak at abs(2*500-80*7)=440 MHz, 8th with frequency 360 MHz and 13th with a peak at abs(13*80-2*500)=40 MHz. Does anyone know how to get rid of these artificial mixing frequencies? One possible way is to increase the sampling frequency to sufficient large value. However, my data set has fixed number of data and time range. So the sampling frequency is actually determined by the property of the data set. Any solutions to this problem?
(I have image for this problem but I don't have enough reputation to post a image. Sorry for bring inconvenience for understanding this question)
You are hitting on a fundamental property of sampling - when you sample data at a fixed frequency fs, you cannot tell the difference between two signals with the same amplitude but different frequencies, where one has f1=fs/2 - d and the other has f2=f2/2 + d. This effect is frequently used to advantage - for example in mixers - but at other times, it's an inconvenience.
Unless you are looking for this mixing effect (done, for example, at the digital receiver in a modern MRI scanner), you need to apply a "brick wall filter" with a cutoff frequency of fs/2. It is not uncommon to have filters with a roll-off of 24 dB / octave or higher - in other words, they let "everything through" below the cutoff, and "stop everything" above it.
Data acquisition vendors will often supply filtering solutions with their ADC boards for exactly this reason.
Long way to say: "That's how digitization works". But it's true - that is how digitization works.
Typically, one low-pass filters the signal to below half the sample rate before sampling. Otherwise, after sampling, there is usually no way to separate any aliased high frequency noise (your high order harmonics) from the more useful spectrum below (Nyquist) half the sample rate.
If you don't filter the signal before sampling it, the defect is inherent in the sample vector, not the FFT.
FIR filter has to be used for removing the noise.
I don't know the frequencies of the noise that might be adding up into the analog feedback signal I am taking.
My apparatus consists analog feedback signal then i am using ADC to digitize the value now I have to apply FIR filter to remove the noise, Now I am not sure which noise the noise which added up in the analog signal from the environment or some sort of noise comes there due to ADC ?
I have to code this in vhdl.(this part is easy I can do that).
My main problem is in deciding the frequencies.
Thanks in Advance !
I am tagging vhdl as some people who are working in vhdl might know about the filter.
Let me start by stating the obvious: An ADC samples at a fixed rate and can not represent any frequency higher than the Nyquist frequency
Step one: understand aliasing, and that any frequency higher than the Nyquist will alias into your signal as noise. Once you get this you understand that you need an anti aliasing filter in your hardware, in your analog signal path before you digitize it. Depending on the noise requirements of the application you may implement a very complicated 4 pole filter using op-amps; the simplest is to use an RC filter.
Step two: setting the filter cut off. Don't set the cutoff right at the Nyquist frequency, make sure the filter is cutting well before the nyquist (1/2x... 1/10x, depends really how clean and how much noise is present)
So now you're actually kind of over sampling your signal: The filter is cutting above your signal, and the sample rate is high enough such that the Nyquist frequency is sufficiently higher. Over sampling is kind of extra data, that you captured with the intent of filtering further, and possibly even decimating (keeping on in N samples and throwing the rest out)
Step three: use a filter to further remove the noise between the initial cut off of the anti-aliasing filter and the nyquist frequency. This is a science on it's own really, but let me start by suggesting a good decimation filter: Averaging 2 values. It's a box-car filter of order 2, also known as a SINC filter, and can be re applied N times. After N times it is the equivalent of an FIR using the values of the Nth row in pascal's triangle (and divided by their sum).
Again, the filter choice is a science on it's own really. To the extreme is the decimation filters of a sigma-delta ADC. The CS5376A datasheet clearly explains what they're doing; I learn quite a bit just from reading that datasheet!
Does anyone know how to use filters in MATLAB?
I am not an aficionado, so I'm not concerned with roll-off characteristics etc — I have a 1 dimensional signal vector x sampled at 100 kHz, and I want to perform a high pass filtering on it (say, rejecting anything below 10Hz) to remove the baseline drift.
There are Butterworth, Elliptical, and Chebychev filters described in the help, but no simple explanation as to how to implement.
There are several filters that can be used, and the actual choice of the filter will depend on what you're trying to achieve. Since you mentioned Butterworth, Chebyschev and Elliptical filters, I'm assuming you're looking for IIR filters in general.
Wikipedia is a good place to start reading up on the different filters and what they do. For example, Butterworth is maximally flat in the passband and the response rolls off in the stop band. In Chebyschev, you have a smooth response in either the passband (type 2) or the stop band (type 1) and larger, irregular ripples in the other and lastly, in Elliptical filters, there's ripples in both the bands. The following image is taken from wikipedia.
So in all three cases, you have to trade something for something else. In Butterworth, you get no ripples, but the frequency response roll off is slower. In the above figure, it takes from 0.4 to about 0.55 to get to half power. In Chebyschev, you get steeper roll off, but you have to allow for irregular and larger ripples in one of the bands, and in Elliptical, you get near-instant cut off, but you have ripples in both bands.
The choice of filter will depend entirely on your application. Are you trying to get a clean signal with little to no losses? Then you need something that gives you a smooth response in the passband (Butterworth/Cheby2). Are you trying to kill frequencies in the stopband, and you won't mind a minor loss in the response in the passband? Then you will need something that's smooth in the stop band (Cheby1). Do you need extremely sharp cut-off corners, i.e., anything a little beyond the passband is detrimental to your analysis? If so, you should use Elliptical filters.
The thing to remember about IIR filters is that they've got poles. Unlike FIR filters where you can increase the order of the filter with the only ramification being the filter delay, increasing the order of IIR filters will make the filter unstable. By unstable, I mean you will have poles that lie outside the unit circle. To see why this is so, you can read the wiki articles on IIR filters, especially the part on stability.
To further illustrate my point, consider the following band pass filter.
fpass=[0.05 0.2];%# passband
fstop=[0.045 0.205]; %# frequency where it rolls off to half power
Rpass=1;%# max permissible ripples in stopband (dB)
Astop=40;%# min 40dB attenuation
n=cheb2ord(fpass,fstop,Rpass,Astop);%# calculate minimum filter order to achieve these design requirements
[b,a]=cheby2(n,Astop,fstop);
Now if you look at the zero-pole diagram using zplane(b,a), you'll see that there are several poles (x) lying outside the unit circle, which makes this approach unstable.
and this is evident from the fact that the frequency response is all haywire. Use freqz(b,a) to get the following
To get a more stable filter with your exact design requirements, you'll need to use second order filters using the z-p-k method instead of b-a, in MATLAB. Here's how for the same filter as above:
[z,p,k]=cheby2(n,Astop,fstop);
[s,g]=zp2sos(z,p,k);%# create second order sections
Hd=dfilt.df2sos(s,g);%# create a dfilt object.
Now if you look at the characteristics of this filter, you'll see that all the poles lie inside the unit circle (hence stable) and matches the design requirements
The approach is similar for butter and ellip, with equivalent buttord and ellipord. The MATLAB documentation also has good examples on designing filters. You can build upon these examples and mine to design a filter according to what you want.
To use the filter on your data, you can either do filter(b,a,data) or filter(Hd,data) depending on what filter you eventually use. If you want zero phase distortion, use filtfilt. However, this does not accept dfilt objects. So to zero-phase filter with Hd, use the filtfilthd file available on the Mathworks file exchange site
EDIT
This is in response to #DarenW's comment. Smoothing and filtering are two different operations, and although they're similar in some regards (moving average is a low pass filter), you can't simply substitute one for the other unless it you can be sure that it won't be of concern in the specific application.
For example, implementing Daren's suggestion on a linear chirp signal from 0-25kHz, sampled at 100kHz, this the frequency spectrum after smoothing with a Gaussian filter
Sure, the drift close to 10Hz is almost nil. However, the operation has completely changed the nature of the frequency components in the original signal. This discrepancy comes about because they completely ignored the roll-off of the smoothing operation (see red line), and assumed that it would be flat zero. If that were true, then the subtraction would've worked. But alas, that is not the case, which is why an entire field on designing filters exists.
Create your filter - for example using [B,A] = butter(N,Wn,'high') where N is the order of the filter - if you are unsure what this is, just set it to 10. Wn is the cutoff frequency normalized between 0 and 1, with 1 corresponding to half the sample rate of the signal. If your sample rate is fs, and you want a cutoff frequency of 10 Hz, you need to set Wn = (10/(fs/2)).
You can then apply the filter by using Y = filter(B,A,X) where X is your signal. You can also look into the filtfilt function.
A cheapo way to do this kind of filtering that doesn't involve straining brain cells on design, zeros and poles and ripple and all that, is:
* Make a copy of the signal
* Smooth it. For a 100KHz signal and wanting to eliminate about 10Hz on down, you'll need to smooth over about 10,000 points. Use a Gaussian smoother, or a box smoother maybe 1/2 that width twice, or whatever is handy. (A simple box smoother of total width 10,000 used once may produce unwanted edge effects)
* Subtract the smoothed version from the original. Baseline drift will be gone.
If the original signal is spikey, you may want to use a short median filter before the big smoother.
This generalizes easily to 2D images, 3D volume data, whatever.