Finding Frequency of wave with variable frequencies

Discussion in 'Math' started by syed_husain, Nov 19, 2009.

  1. syed_husain

    Thread Starter AAC Fanatic!

    Aug 24, 2009
    could anyone help me to find the frequency and amplitude of this following function:

    A*cos(w*t)+ B*sin(x*t)+C*sin(y*t). where A,B,C & w,x,y are three different amplitudes & frequencies respectively.

    thnx in advance.

    N.B. i am guessing fourier transform should be used. i did a course in intro to signal but i did not quite grasp the concept of the FT. if anyone knew a method besides FT, for example, using trigonometric manipulations i will be really grateful.
  2. Papabravo


    Feb 24, 2006
    I'll give you a starting hint. When you multiply two sine waves together of different frequencies you get output components with the two original frequencies and there is an output component at the sum of the two frequencies and another at the difference of the two frequencies. These four componets will be added to the cosine wave. Does that help?
  3. davebee

    Well-Known Member

    Oct 22, 2008
    While that is true, papabravo, it looks like this particular function is not multiplying sines.

    Inside the trig functions, time multiplies cycles per second to yield cycles as an angle, then the sine or cosine of that angle is taken, then the result, which is in the range -1 to 1, is multiplied by an amplitude factor. The sine and cosine functions themselves are not multiplied by each other, only added.

    When sine waves are added, no new frequencies are generated. The result of doing this addition should be a signal that contains only the three original frequencies. The actual wave itself may appear to be quite a complex mixture of signals, but mathematically the signals just add.

    The amplitude at any point in time will just be the sum of the amplitude of the individual signals at that time.
  4. Papabravo


    Feb 24, 2006
    I could swear that I saw a multiplication sign between the two sine functions. As my heroine Emily Latella would say "Never mind!"
  5. syed_husain

    Thread Starter AAC Fanatic!

    Aug 24, 2009
    so, what i understand that it is not possible to combine this kind of function into a single sinusoid form like A*sin(ω*t+θ). am i right?

    and for the frequency, i plot a simple function cos(t)+sin(2t) in the excel. from there i chose what value is at t=0.63 and scroll down to find the same value at t=6.93. so, the period is 6.29 s. hence frequency is (2*pi)/6.29 = 0.906 rad/sec. so, the resultant sinusoid will have a new frequency of 0.906 rad/sec. a totally new frequency. and the magnitude would be 1.76. but i don't know about the phase.

    i don't know whether i am making a simple thing more complex. any advice will be much appreciated.

  6. someonesdad

    Senior Member

    Jul 7, 2009
    This same basic question popped up on another thread a week or two ago. To my knowledge, there is no closed-form expression for

    sin a + b sin c

    which is what you'd use to reduce/change your original expression. Note, however, there is one for sin a + sin b.

    It's pretty straightforward to use a programming tool to plot such functions to see how they behave. Here's a quickie example I wrote in python using numpy and scipy:

    Code ( (Unknown Language)):
    2. from pylab import *
    4. t = arange(0, 5*pi, 0.01)
    5. A, B, C = 1.1, 2.2, 3.3
    6. w, x, y = 3.3, 2.2, 1.1
    7. plot(t, A*cos(w*t)+ B*sin(x*t)+C*sin(y*t))
    8. grid(True)
    9. savefig("sinusoid_sum.png")
    It made the attached figure.

    I do this kind of thing so much I have a shell script that creates a boilerplate python script to plot a function.
  7. syed_husain

    Thread Starter AAC Fanatic!

    Aug 24, 2009
    thnx guys. now i understand that u can't wirte this kind function in a single sinusoid.