Hamming window
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From: rajgerman on 26 Feb 2006 11:01 Thanks guys I have understood the hamming window and also have implemented it. I'm having difficulty labelling my axis. I have converted the complex numbers of ffted data (X) to real values by applying the conjugate (Z). I'm having difficulty labelling and converting my x axis. I need to represent it in frequency terms. Data = Z Sample rate = 44100Hz Total no. of frequencies/values of data = 88200 Length of signal = 2 seconds I have also applied fftshift to the data (Z) so that my left half is negative and the right half is positive. How can I represent the x-axis in frequency terms?? If someone could also tell me how I will be able to get rid of certain frequencies e.g. I want everything below 20Hz to be cut off/throw it away??
From: Fred Marshall on 26 Feb 2006 22:12 "rajgerman" <rajgerman(a)msn.com> wrote in message news:0eCdnVM_-79bTZzZRVn-pg(a)giganews.com... > Thanks guys I have understood the hamming window and also have implemented > it. > > I'm having difficulty labelling my axis. I have converted the complex > numbers of ffted data (X) to real values by applying the conjugate (Z). Why? > > I'm having difficulty labelling and converting my x axis. I need to > represent it in frequency terms. > > Data = Z > Sample rate = 44100Hz > Total no. of frequencies/values of data = 88200 > Length of signal = 2 seconds Each frequency value is 1/(Length of signal) apart = 1/2 Hz. This is also understood from sample rate 44100 divided by number of values 88200 = 44100Hz / 88200samples = 0.5Hz/sample Actually, because things are sampled I try to keep track by understanding "data points or samples" AND "intervals" So, 44100 sample rate for 2 seconds starts at time=0 and ends at time = (2-1/44100). There are 44100-1 intervals in between but normal assumptions add an interval after the last sample (and then the sequence is assumed to repeat). So, then there are 44100 intervals that encompass 2 seconds. > > I have also applied fftshift to the data (Z) so that my left half is > negative and the right half is positive. Why? The normal representation is from zero to fs/2 and from fs-fs/2 to fs which is the same as from -fs/2 to zero. So it goes from zero to fs-fs/(length of signal) and is assumed to repeat at fs with F(fs) = F(0). > > How can I represent the x-axis in frequency terms?? > As above. > If someone could also tell me how I will be able to get rid of certain > frequencies e.g. I want everything below 20Hz to be cut off/throw it > away?? High pass filter. If you're doing it in the frequency domain then it's best to multiply by the complex frequency response of an actual FIR filter - not just multiply by zero where you want things to go away. Fred
From: rajgerman on 28 Feb 2006 11:12 Hey Fred I didn't quite understand your explanation. I applied fftshift so that it looks more simple. Now my data goes from -fs to 0 and then from 0 to fs. I know that the negative half is just a mirror image of the other side. All I need to know is how to represent the x-axis in frequency terms?? What would be the coding?? Thanks for your help.
From: Fred Marshall on 1 Mar 2006 11:27
"rajgerman" <rajgerman(a)msn.com> wrote in message news:_sWdnTxyGJPA65nZnZ2dnUVZ_tWdnZ2d(a)giganews.com... > Hey Fred > > I didn't quite understand your explanation. > > I applied fftshift so that it looks more simple. Now my data goes from -fs > to 0 and then from 0 to fs. I know that the negative half is just a mirror > image of the other side. All I need to know is how to represent the x-axis > in frequency terms?? What would be the coding?? Do you mean you want someone to write the code for you? I'll bet Google would result in a listing for you. Here's how it might go: Make a vector that has the x values according to the frequency sample spacing. Spacing=1/T where T is the length of the signal ... that's what I tried to tell you in my last post. x(i)=(1/T)*(i-1) Is that all you're asking? As far as applying fftshift it's important to understand your objective. I would not do it if I were just doing signal processing. However, if the objective is to make "pretty pictures" then OK. Then you have to modify the x vector from above of course but that's a very simple matter. You may also consider repeating the value at fs/2 at each end so there are N+1 samples in order to make the picture symmetrical around zero. Examples: If there are 100 samples going from zero to fs-1/T and you circularly shift them by N/2 then the zeroeth sample will be at x2=51, the 100th sample will be at x2=50 and the the 51st sample will be at x2=1 and the 50th sample will be at x2=100. This isn't symmetrical. It looks like this: x1(1) == 0 x1(2) == 1/T x1(51) == fs/2 x1(100) == fs-1/T repeats at x1(1) == fs.... Shifting by N/2 = 50: x2(1) == fs/2 x2(51) == 0 x2(100) = fs/2-1/T repeats at x2(1) == fs/2 So, you may wish to add another point just so it's symmetrical: x2(101) == fs/2 and add the corresponding value to the y vector in the plot. It that what you mean? Now, if N is odd, then there won't be a value that corresponds to frequency = fs/2 at all because fs/2 is not an integer multiple of 1/T. For N=101 you will have: x1(1) == 0 x1(2) == 1/T .. x1(51) == fs/2 - 1/2T x1(52) == fs/2 + 1/2T .. x1(101) == fs - 1/T repeats at x1(1) == fs .... Shifting by fs/2 corresponds to a shift of an odd integer multiple of 1/2T, and causes the samples to align on odd intervals of 1/2T and we need a new definition for x2 so I will define x3 to have 2*N samples = 202 samples. We will get that by adding an extra samples in the x1 vector to get x1' and adding zeros in the y value vector. Then you can shift by 101 samples: Start with x1'(1) == 0 x1'(2) == 1/2T with a zero value in the y values to be plotted x1'(3) == 1/T .. x1'(100) == fs/2- 1/2T .. which is an integer multiple of 1/T x1'(101) == fs/2 with a zero value in the y values to be plotted x1'(102) == fs/2 + 1/2T .. which is an integer multiple of 1/T .. x1'(201) == fs - 1/T repeats at x1(1) == fs .... x1'(202) == fs - 1/2T which is a sample added to fill in the array with a zero value in the y values to be plotted Now shift to get x3(103) == 0 ... this means a shift of 102: x3(1) == fs/2 with a zero value in the y values to be plotted .. x3(103) == 0 .. x3(202) = fs/2-1/2T repeats at x3(1) == fs/2 So, you may wish to add another point just so it's symmetrical: x2(203) == fs/2 and add the corresponding zero value to the y vector in the plot. If I didn't make any mistakes then that's it. Fred |