Post by cheeki on Nov 9, 2005 4:26:40 GMT -5
Dear charan,
please help me in understanding the following:
1- we have a sine wave whose frequency is 5 Hz when we take the samples and then analyze the fourier spectrum what we get is a different frequency. the signal is the same just sampled in time.
2- why do we take the fundamental frequency or the resolution frequency equal to the ratio of sampling frequency and number of samples
3- why the fourier spectrum repeats after every N that is the total number of samples.
4- the new frequncy of the sampled discrete signal is now at frequency of the sine wave divided by sampling frequency multiplied by the total number os samples. lets say the frequency of the sine wave wasf1= 5 Hz and we sampled it atfs= 20 Hz so we get 4 samples in one period. and we wish to take the discrete fourier transform of N=8 samples . In frequency domain we get a signal at f1/fs*n=5/20*8=2 Hz so at two we have signal . the spectrum of the signal has changed also why it is said that if the resultant does not appear to be an integer there shall be spectral leakage. what is this all stuff about.
In your tutorial i have learnt that we multiply sampled wave with exponential sample wave of fundamental frequency equal to the ratio of the sampling frequency and total number of samples. and then take the area under the resultant wave if there is a positive area then we say that that frequency component is present in the signal and we can go on successively from here incrementing our resolution frequncy with integrat multiples . how should i develop from here to learn the above facts. Please correct me if i am wrong also explain me the periodicity of the discrete fourier transform.
3- my teacher says that if the signal is discrete in time domain it will have continuous spectrum in frequency domain. what i know is that if you let the period of the signal to be infinite then the fundamental frequency becomes very small such that the integral multiples become continuous. but what it has to do with discretizing the signal it just does not make sense that a discrete signal shall have a continuous spectrum and a continuous signal shall have discrete signal.
4- also please do tell me the effects that the spectrum will have if the same discrete signal is made periodic .
Please help me as i am stuck here .i have read different books and tutorials but cant just get the thing correct also cant get time from my busy teachers.
yours respectfully
cheeki
please help me in understanding the following:
1- we have a sine wave whose frequency is 5 Hz when we take the samples and then analyze the fourier spectrum what we get is a different frequency. the signal is the same just sampled in time.
2- why do we take the fundamental frequency or the resolution frequency equal to the ratio of sampling frequency and number of samples
3- why the fourier spectrum repeats after every N that is the total number of samples.
4- the new frequncy of the sampled discrete signal is now at frequency of the sine wave divided by sampling frequency multiplied by the total number os samples. lets say the frequency of the sine wave wasf1= 5 Hz and we sampled it atfs= 20 Hz so we get 4 samples in one period. and we wish to take the discrete fourier transform of N=8 samples . In frequency domain we get a signal at f1/fs*n=5/20*8=2 Hz so at two we have signal . the spectrum of the signal has changed also why it is said that if the resultant does not appear to be an integer there shall be spectral leakage. what is this all stuff about.
In your tutorial i have learnt that we multiply sampled wave with exponential sample wave of fundamental frequency equal to the ratio of the sampling frequency and total number of samples. and then take the area under the resultant wave if there is a positive area then we say that that frequency component is present in the signal and we can go on successively from here incrementing our resolution frequncy with integrat multiples . how should i develop from here to learn the above facts. Please correct me if i am wrong also explain me the periodicity of the discrete fourier transform.
3- my teacher says that if the signal is discrete in time domain it will have continuous spectrum in frequency domain. what i know is that if you let the period of the signal to be infinite then the fundamental frequency becomes very small such that the integral multiples become continuous. but what it has to do with discretizing the signal it just does not make sense that a discrete signal shall have a continuous spectrum and a continuous signal shall have discrete signal.
4- also please do tell me the effects that the spectrum will have if the same discrete signal is made periodic .
Please help me as i am stuck here .i have read different books and tutorials but cant just get the thing correct also cant get time from my busy teachers.
yours respectfully
cheeki