Main Question or Discussion Point
For the discrete complex sinusoid with period N, how many distnict sinusoids are there? And why?
I guess "discrete" has some meaning in DSP that i don't know.I meant in terms of the frequency how many distinct sinusoids are there for discrete
The SineWave object generates a discrete-time sinusoid. The sine wave object generates a real–valued sinusoid or a complex exponential. A real-valued, discrete-time sinusoid is defined as:
where A is the amplitude, f is the frequency in hertz, and φ is the initial phase, or phase offset, in radians.
A complex exponential is defined as:
For both real and complex sinusoids, the amplitude, frequency, and phase offsets can be scalars or length-N vectors, where N is the desired number of channels in the output. When you specify at least one of these properties as a length-N vector, scalar values specified for the other properties are applied to each of the N channels.
one per amplitude.http://www.mathworks.com/help/dsp/ref/sinewave.html said:Generating Multichannel Outputs
For both real and complex sinusoids, the Amplitude, Frequency, and Phase offset parameter values (A, f, and ϕ) can be scalars or length-N vectors, where N is the desired number of channels in the output. When you specify at least one of these parameters as a length-N vector, scalar values specified for the other parameters are applied to every channel.
For example, to generate the three-channel output containing the real sinusoids below, set Output complexity to Real and the other parameters as follows:
y1 = sin(2000πt) ; (channel 1)
- Amplitude = [1 2 3]
- Frequency = [1000 500 250]
- Phase offset = [0 0 pi/2]
y2 = 2sin(1000πt) ; (channel 2)
y3 = 3sin(500πt+π2) ; (channel 3)
I was referring to e^jwn (where w is the angular frequency) as the complex sinusoid (thats how my book refers to it, i honestly thought it was not an ambiguous term)Well, I'm not certain what he is asking. If he really means complex sine, that just complicates things ;)
Thank you for the effort you spent here, but its my fault for not expressing the question unambiguouslyI guess "discrete" has some meaning in DSP that i don't know.
Are you asking in reference to a computer program of some sort ?
I'm guessing it's user defined
You defined frequency as 1/N
one per amplitude.
But i am likely way off target , so will await a better informed response.
Time depedent sine function fn(t)=An⋅sin(ωn⋅t+φn) can be represented by a time depedent complex number in a complex plane, the rotating phasor zn(t):And i observed with an oscilloscope the truism that when you add two sinewaves you get just another sinewave.
So in my simple world, any sinewave can be broken into its real and imaginary parts but it's still just one sinewave.
This tutorial agrees in the second slide, page 2 of 22, with my understanding ,of course in terms of t not n,
so e^(jwn) to me represents one sine function, represented by that rotating phasor.
To me they rotate in time; what would rotating in 'n' mean physically i can't say.
so i would answer your question: one.
But i'm no Euler.
Sorry, I don't understand what you're trying to askFor the discrete complex sinusoid with period N, how many distnict sinusoids are there? And why?
Of course - i neglected to add that condition.Superposition of two or more sine functions gives another sine function only if their frequencies are equal
I know that you know/understand this, but I'm not sure for OP. Maybe this remark could help him.Of course - i neglected to add that condition.
adding different frequency sines gives a
I've done that both with oscilloscope in high school and decades later with Fourier in Basic.
Thanks, zoki that helps me a lot.
In my opinion the answer to the OP can be either 1 or 2, depending on the interpretation of counting “how many” and the meaning of “distinct sinusoid”. The term “discrete complex sinusoid” is singular.For the discrete complex sinusoid with period N, how many distnict sinusoids are there? And why?
What do you mean by "point"?Basically, if there are 128 points in your original discrete time waveform, there will be 128 points in your discrete fourier transform.