Hi, I have a quantized input audio signal file (.wav). I want to convert the sampling rate from 11025 Hz to 24000. I know that I have to upsample the signal, lowpass filter and downsample it. But how can I find the converting ratio? Is it 11025/24000 or 24000/11025? And I am new to DSP and also Matlab. So, anyhelp to write this sys in Matlab?Please help if you can. thanks a lot in advance!!!
Help for sampling rate converter
Started by ●January 24, 2008
Reply by ●January 24, 20082008-01-24
On Jan 24, 12:29 pm, "hsquared" <hnin...@yahoo.com> wrote:> Hi, > > I have a quantized input audio signal file (.wav). > I want to convert the sampling rate from 11025 Hz to 24000. > I know that I have to upsample the signal, lowpass filter and downsample > it.You don't have to. You could just interpolate any samples needed using various splines, or a Sinc or windowed-Sinc kernel. IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M
Reply by ●January 24, 20082008-01-24
First do an upconversion by 2. With this the new sample rate will be 22050 Hz. now the problem is the handover of data from 22050 Hz to 24000 Hz. This can be solved by means of polynomial interpolation of 3rd order. meaning take 4 adjacent samples and apply polynomial interpolation. one of the best polynomials for your application are "catmull-rom" also known as "4 point, 3rd order Hermite". Search on the web and you will get the equations. reference: http://ccrma.stanford.edu/~jos/resample/ Regards Bharat Pathak www.arithos.com ~dsp Simplified>On Jan 24, 12:29 pm, "hsquared" <hnin...@yahoo.com> wrote: >> Hi, >> >> I have a quantized input audio signal file (.wav). >> I want to convert the sampling rate from 11025 Hz to 24000. >> I know that I have to upsample the signal, lowpass filter anddownsample>> it. > >You don't have to. You could just interpolate any >samples needed using various splines, or a Sinc or >windowed-Sinc kernel. > > >IMHO. YMMV. >-- >rhn A.T nicholson d.0.t C-o-M >
Reply by ●January 25, 20082008-01-25
Ron wrote:> hsquared wrote: > > > Hi, > > > I have a quantized input audio signal file (.wav). > > I want to convert the sampling rate from 11025 Hz to 24000. > > I know that I have to upsample the signal, lowpass filter and downsample > > it. > > You don't have to. �You could just interpolate any > samples needed using various splines, or a Sinc or > windowed-Sinc kernel.Ron Signal resampling using kernel-interpolation (e.g. sinc, polynomials, dirichlets, gaussian, etc.) is a special case of the upsampling, filtering and downsampling procedure. Don't you agree? @h^2: http://ccrma.stanford.edu/~jos/resample/ Regards, Andor
Reply by ●January 25, 20082008-01-25
On Thu, 24 Jan 2008 14:29:05 -0600, "hsquared" <hnin720@yahoo.com> wrote:>Hi, > >I have a quantized input audio signal file (.wav). >I want to convert the sampling rate from 11025 Hz to 24000. >I know that I have to upsample the signal, lowpass filter and downsample >it. >But how can I find the converting ratio? Is it 11025/24000 or >24000/11025? >And I am new to DSP and also Matlab. So, anyhelp to write this sys in >Matlab?Please help if you can. > >thanks a lot in advance!!!Hello hsquared, to make life a little easier for yourself, you can upsample by 320, lowpass filter, and then downsample by 147. I thought I could throw a little MATLAB code together to help you. However, that initial interpolation by 320 requires an FIR filter that has over a thousand taps. Dealing with such filters makes me nervous. For being new to DSP, and new to MATLAB, you sure picked an "exciting" problem to work on. I suggest you upsample/filter in multiple stages so as to keep your filters of a reasonable length. Perhaps upsample/filter by 10 and then 32 (10*32=320). Or possibly upsample/filter by 8, by 8 again, and by 5 (8*8*5=320). Sorry hsquared but I don't have the time to figure out exactly what's best to do right now. Below is some code, but it's not working terribly well. Good Luck, [-Rick-] --------------- % Code for hsquared from Rick Lyons clear, clc Fs_in = 11025; Fs_out = 24000; Nsamples = 500; % Number of time samples Time = (0:Nsamples-1)/Fs_in; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Create an Input (time-domain) sequence %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ToneFreq = 2*1102.5; % Freq of test tone Input = cos(2*pi*ToneFreq*Time); % Input sequence % plot Input sequence figure(1) subplot(2,1,1) plot(Time, Input, '-bo','markersize', 4) axis([0, max(Time), 1.2*min(Input), 1.2*max(Input)]) title('Input Seq.') grid on, zoom on %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Upsample by 320 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% U = 320; % Upsample factor Upsampled = zeros(size(1:U*length(Input))); % Upsampled sequence Upsampled([1:U:length(Upsampled)]) = Input; Upsampled = Upsampled(1:length(Upsampled) -U +1); % Truncate trailing zeros %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Design linear-phase lowpass FIR filter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NumTaps = 1295; % Number of FIR filter taps B = fir1(NumTaps, (2/U)*Fs_in/Fs_out); % Filter coeffs % plot filter freq response figure(2) freqz(B, 1, 512, U*Fs_in) % plotting command zoom on %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Filter the upsampled sequence %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Filter_out = filter(B, 1, Upsampled); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Downsample by 147 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% D = 147; % Decimation factor Output = Filter_out(1:D:length(Filter_out)); % Final output % plot Output sequence Time_new = (0:length(Output)-1)/Fs_out; % New time vector for plotting figure(1) subplot(2,1,2) plot(Time_new, Output, '-ro','markersize', 4) axis([0, max(Time_new), 1.2*min(Output), 1.2*max(Output)]) title('Output Seq.') grid on, zoom on
Reply by ●January 25, 20082008-01-25
On Jan 25, 4:53 am, Andor <andor.bari...@gmail.com> wrote:> Ron wrote: > > hsquared wrote: > > > > Hi, > > > > I have a quantized input audio signal file (.wav). > > > I want to convert the sampling rate from 11025 Hz to 24000. > > > I know that I have to upsample the signal, lowpass filter and downsample > > > it. > > > You don't have to. You could just interpolate any > > samples needed using various splines, or a Sinc or > > windowed-Sinc kernel. > > Ron > > Signal resampling using kernel-interpolation (e.g. sinc, polynomials, > dirichlets, gaussian, etc.) is a special case of the upsampling, > filtering and downsampling procedure.Hi Andor, I tend to think the reverse: e.g. up/down sampling with filtering seems like a special case implementation of kernel interpolation. Is there a reason we are parsing "special case of" differently? Perhaps it's because I studied numerical methods before I learned any practical DSP theory? IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M
Reply by ●January 25, 20082008-01-25
On 25 Jan., 19:15, "Ron N." <rhnlo...@yahoo.com> wrote:> On Jan 25, 4:53 am, Andor <andor.bari...@gmail.com> wrote: > > > > > > > Ron wrote: > > > hsquared wrote: > > > > > Hi, > > > > > I have a quantized input audio signal file (.wav). > > > > I want to convert the sampling rate from 11025 Hz to 24000. > > > > I know that I have to upsample the signal, lowpass filter and downsample > > > > it. > > > > You don't have to. �You could just interpolate any > > > samples needed using various splines, or a Sinc or > > > windowed-Sinc kernel. > > > Ron > > > Signal resampling using kernel-interpolation (e.g. sinc, polynomials, > > dirichlets, gaussian, etc.) is a special case of the upsampling, > > filtering and downsampling procedure. > > Hi Andor, > > I tend to think the reverse: e.g. up/down sampling with > filtering seems like a special case implementation of > kernel interpolation.Well, every kernel interpolation can be written as an upfirdn- procedure (exercise to the reader: given a kernel psi(t), what is the filter in the upsample-filter-downsample procedure for rational sampling rate changes?). It just occured to me that the opposite is true as well (although given a filter, the equivalent interpolation kernel is not unique).> > Is there a reason we are parsing "special case of" > differently? �Perhaps it's because I studied numerical > methods before I learned any practical DSP theory?Regards, Andor
Reply by ●January 26, 20082008-01-26
On Thu, 24 Jan 2008 14:29:05 -0600, "hsquared" <hnin720@yahoo.com> wrote:>Hi, > >I have a quantized input audio signal file (.wav). >I want to convert the sampling rate from 11025 Hz to 24000. >I know that I have to upsample the signal, lowpass filter and downsample >it. >But how can I find the converting ratio? Is it 11025/24000 or >24000/11025? >And I am new to DSP and also Matlab. So, anyhelp to write this sys in >Matlab?Please help if you can. > >thanks a lot in advance!!!Hello hsquared, did you ever solve your interpolation problem? [-Rick-]
Reply by ●January 27, 20082008-01-27
Rick Lyons wrote:> you can upsample by 320, lowpass filter, and > then downsample by 147.Wow, excuse me, but why do you suggest that? That's horrible to encourage such practices, and it makes interpolation by a non-integer ratio much harder than it is. Here's what I would suggest instead : First, define how precise a filtering you want by choosing how large a windowed sinc function you would use (in numbers of bins). We'll call this value sincsize (sorry about the poor naming scheme). Go through each sample of your new, interpolated signal you're trying to create. Now, for each of these new samples, calculate the position it matches to in the original signal (for example, if you're at sample index 100 in the new signal, you'll get the value 100 * 11025 / 24000 = 45.9375, but let's call this value indexA). Now, go through each original sample between indexes calculated by indexA - (sincsize/2) (rounded up to the next integer number) and indexA + (sincsize/2) (rounded down, or if you prefer truncated). Weight the value at these indexes (which we'll call indexX) using a windowed sinc centered on indexA. The formula giving for that would be, using the Blackman function as a window, in C-ish pseudo-code: weighted_value = original_signal[indexX] * (0.42 - 0.5*cos(2*pi * (indexX-indexA) / sincsize) + 0.08*cos(4*pi * (indexX-indexA) / sincsize)) * sin(2*pi*0.5 * (indexX-indexA)) / (indexX-indexA) You would sum every of these weighted values into the value in the new signal at indexA, and do that for every integration of indexA. Thus, you would simply and efficiently interpolate by a non-integer resampling ratio using a variant of time-domain convolution by a windowed sinc FIR. I only hope I didn't lose anyone during the course of my explanation.
Reply by ●January 27, 20082008-01-27
Erratum : Michel Rouzic wrote:> it makes interpolation by a non-integer > ratio much *SOUND* harder than it is.> weighted_value = original_signal[indexX] * (0.42 - 0.5*cos(2*pi * > (indexX-indexA) / sincsize) + 0.08*cos(4*pi * (indexX-indexA) / > sincsize)) * sin(2*pi*0.5 * (indexX-indexA)) / (indexX-indexA)More like : weighted_value = original_signal[indexX] * (0.42 - 0.5*cos(2*pi * ((indexX-indexA) / sincsize + 0.5)) + 0.08*cos(4*pi * ((indexX- indexA) / sincsize + 0.5)) * sin(2*pi*0.5 * (indexX-indexA)) / (indexX- indexA) I always forget that the Blackman function doesn't peak at x = 0.0 but at half its size.
