On a side note
Totally irrelevant
If you don't have information of the phase of the signals, you'll not be able to reconstruct the waveform.
I don't know what your "Excel and Fourier analysis tool" is, but it should give you frequency and magnitude as well as phase information. Otherwise you're lost...
It is very relevant if we are talking about audio applications.
Where on earth did you find a reference to audio in the original question?
But keep in mind that it is better to add audio signals in a way that minimises peak amplitude to avoid clipping.
Presumably these all start at the same point in time? As all the information I have is the harmonic frequency and it's magnitude. So if a waveform were to start earlier or later rather than all of the cycle start together then it would not work out would it?
Attached are the questions and the spreadsheet they provide, so I have run the excel analysis tool as requested, the harmonic distortion I make to be something like 89%. I don't know if the fact that results are given in complex numbers effectively give me more information about phase angles. it looks like as usual the questions open more cans of worms than I was taught to close by the module so I'm back on the road again.
The point of the exercise is to understand that the Fourier transform and its inverse are both integrals in the continuous case and sums in the discrete case. The forward and inverse transforms differ by a scaling factor (i prefer sqrt(N) which is symmetric) and the sign of the exponent of the exponential. Both signs are used for the forward and inverse transforms by different groups of people.
. I don't know if the fact that results are given in complex numbers effectively give me more information about phase angles. it looks like as usual the questions open more cans of worms than I was taught to close by the module so I'm back on the road again.
So I'm a little confused as to why 17.5 Hz is the fundamental. I thought that the Fourier analysis showed you the strength of any particular frequency in a waveform. And in this case the first strongest waveform is at 52.73 Hz is there anything in particular I'm missing in this whole mess?
Isn't the first significant frequency the fundamental? Why would fundamental be at 17.5 Hz? From what I can tell it just happens to be related to the amount of samples they have taken? I'm rereading their explanation of how to use Excel tool maybe they have hidden some clue there as to how I am supposed to solve this particular problem
What I could really do with is a shed load of time to study the subject properly instead I've been given a crash course and then this assignment so I can just move on and get my silly piece of paper. The fact that a silly piece of paper doesn't actually mean anything is of no interest to anybody I just need a silly piece of paper. The result is that I going round in circles trying to understand the subject properly rather than just pass the test.
. I don't know if the fact that results are given in complex numbers effectively give me more information about phase angles. it looks like as usual the questions open more cans of worms than I was taught to close by the module so I'm back on the road again.
You seem to expect them to ask a question and tell you the answer. This is all *very* basic stuff.
Perhaps you should review the definition of the discrete and continuous Fourier transforms.
The discrete transform is defined on the semiclosed interval [-Pi:Pi} and periodic outside that interval. It repeats on [Pi:2*Pi), etc. There is no requirement that the signal be periodic inside [-Pi:Pi).
The subtlety of the semiclosed interval and its consequences are often neglected, but I shall leave that to the reader. along with the proper treatment of the amplitudes of the first and last sample and the effects of series length and window choice.
As remarked before, the appropriate tool is Octave, MATLAB or similar. I am a little disturbed that you were encouraged to use Excel for such work.
So I'm a little confused as to why 17.5 Hz is the fundamental. I thought that the Fourier analysis showed you the strength of any particular frequency in a waveform. And in this case the first strongest waveform is at 52.73 Hz is there anything in particular I'm missing in this whole mess?There is no law that says the first fundamental has to be the biggest. If you look at every frequency, they exactly equal 17.5... x2, x3, x4, x5 up to x1022. That is why 17.5... is the fundamental and every other frequency is a harmonic.
The other thing if the inverse transform will try and make a repetitive waveform looking like the original samples but repeated. What frequency will this waveform have? It has to be 17.5... Hz. There is no lower frequency. It definitely cannot be higher - the 17.5... component would then prevent the second waveform repetition from beeing the same as the first. That means the original 1024 samples must have been taken during one 17.5... Hz period.QuoteIsn't the first significant frequency the fundamental? Why would fundamental be at 17.5 Hz? From what I can tell it just happens to be related to the amount of samples they have taken? I'm rereading their explanation of how to use Excel tool maybe they have hidden some clue there as to how I am supposed to solve this particular problem
What I could really do with is a shed load of time to study the subject properly instead I've been given a crash course and then this assignment so I can just move on and get my silly piece of paper. The fact that a silly piece of paper doesn't actually mean anything is of no interest to anybody I just need a silly piece of paper. The result is that I going round in circles trying to understand the subject properly rather than just pass the test.It looks like Excel may not have an Inverse Fourier Transform, but you can look on Youtube tutes for clues. I do not use Excel. You may have to load the Data Analysys pack into Excel, and there may be both FFT and DFT. I do not know.
You can also use the sum of the cos + sin equations I mentioned not long ago, but that will need a bit if Excel skill. You have to do formulas with a variable in excel and loop it over 1024 values of t.
If you don't want to do any of it, that is fine with me. It is actually worth learning.