How Do You Calculate Frequency from Period?

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SUMMARY

The discussion centers on calculating frequency from a given period, specifically a period of 11 years. The formula used is T = 1/f, where T is the period and f is the frequency. The participants clarify that frequency should be expressed in Hertz (Hz), which is 1/seconds, and they discuss the design of a low-pass Butterworth filter based on this frequency. The conversation also touches on the Nyquist frequency, which is relevant for determining the cutoff frequency in filter design.

PREREQUISITES
  • Understanding of the relationship between period and frequency using T = 1/f
  • Knowledge of signal processing concepts, particularly low-pass filters
  • Familiarity with Butterworth filter design and its polynomial functions
  • Basic grasp of Nyquist frequency and its significance in sampling
NEXT STEPS
  • Learn how to convert periods in years to frequency in Hz
  • Research the design principles of Butterworth filters and their applications
  • Explore the concept of Nyquist frequency and its role in digital signal processing
  • Investigate the differences between FIR and IIR digital filters
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Signal processing engineers, data analysts, and anyone involved in designing digital filters or analyzing time-series data with periodic components.

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Given I know the period of a signal how do I find the frequency






Heres what I know

Period = 10 years so using T = 1/f where f = frequency would that give me 1/10??
 
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Please any feedback would be great.
 


andrey21 said:
Given I know the period of a signal how do I find the frequency






Heres what I know

Period = 10 years so using T = 1/f where f = frequency would that give me 1/10??

The standard unit of frequency is Hz (Hertz), which is 1/seconds. Not 1/years.

Can you convert the period of 10 years into Hz? (It will be a very small number)
 


Thank you for moving my post berkeman, I think I may have made an error with the question. I was asked to determine the frequency that corresponds to the period observed in a data set. Given the period is 10 years, I am basically trying to find the cutoff frequency. If that makes any sense.
 


andrey21 said:
Thank you for moving my post berkeman, I think I may have made an error with the question. I was asked to determine the frequency that corresponds to the period observed in a data set. Given the period is 10 years, I am basically trying to find the cutoff frequency. If that makes any sense.

Doesn't make sense to me yet. What do you mean by cutoff frequency? I'm familiar with that term in filter design. What is the dataset?
 


Yes well I have been asked to design a low pass filter, given that i know period of 10 years and sampling interval of 1 month.
 


andrey21 said:
Yes well I have been asked to design a low pass filter, given that i know period of 10 years and sampling interval of 1 month.

What order digital filter do you plan to design? Which polynomial will you choose and why?

Other than the very low frequencies involved, it sounds like a straightforward digital filter design.
 


Well I've been told either 4 or 5th order. What do you mean by polynomial?
 
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andrey21 said:
Well I've been told either 4 or 5th order. What do you mean by polynomial?

The filter functions are polynomial functions, and there are several different forms of the polynomials to choose from. You choose which one (like Cheby, Butterworth, etc.) based on what you are trying to optimize in your filter's response.

More here:

http://en.wikipedia.org/wiki/Filter_(signal_processing )

.
 
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  • #10
Oh I understand I was planning on using a Butterworth filter.
 
  • #11
I actually have a programme tht will do most of the calculation for me I just need to work out a cutoff frequency and the order which is either 4 or 5.
 
  • #12
andrey21 said:
I actually have a programme tht will do most of the calculation for me I just need to work out a cutoff frequency and the order which is either 4 or 5.

Well, what do you think you should choose for a cutoff frequency? What is the tradeoff with a Butterworth filter in choosing the cutoff closer and closer to the frequency region of interest?
 
  • #13
Im not to sure but I have to get it in terms of degrees, for example 0.2PI = 36 degrees etc...
 
  • #14
andrey21 said:
Im not to sure but I have to get it in terms of degrees, for example 0.2PI = 36 degrees etc...

Sorry, get what in terms of degrees? Degrees would relate to some phase. But you are asking about filtering in the time domain according to a frequency characteristic (the filter)...
 
  • #15
Rite I think I am nt explaining myself very well so I will read the question. Using the figure (period) as a filter cutoff period together with known sampling interval (1 month) design a low pass filter to remove higher frequencies.
 
  • #16
andrey21 said:
Rite I think I am nt explaining myself very well so I will read the question. Using the figure (period) as a filter cutoff period together with known sampling interval (1 month) design a low pass filter to remove higher frequencies.

Can you post a copy of the figure?
 
  • #17
Figure? U mean the period? If so it is 11 years.
 
  • #18
andrey21 said:
Rite I think I am nt explaining myself very well so I will read the question. Using the figure (period) as a filter cutoff period together with known sampling interval (1 month) design a low pass filter to remove higher frequencies.

andrey21 said:
Figure? U mean the period? If so it is 11 years.

No, you said "using the figure", so I thought there was a figure that graphed the data as s function of time. It must be a semantics thing -- it looks like the word figure was used as a synonym of period?

So they want you to use the number given as the period to come up with the cutoff frequency. Well, that's just the simple math we talked about at the beginning of the thread. Use your f = 1/T equation, and be careful to use units of Hz (1/s) for frequency. You will get a cutoff frequency of some number much less than 1Hz, but that doesn't matter.

Then just use your filter design software to design the coefficients for the Butterworth polynomial. Are you using an FIR or IIR digital filter?
 
  • #19
So I have to convert 1/11 years into Hz per second?
 
  • #20
andrey21 said:
So I have to convert 1/11 years into Hz per second?

1/(11 years) = 1/(how many seconds?) = ?? * 10^-?? Hz
 
  • #21
Hi berkeman I think the answer you are trying to help me find isn't the correct one, having re read the question and the information provided.

Basically I have:

A period of 11 years

A Nyquist frequency of 1/2 month (as sampling interval is one month, using 1/2(delta t)
I am asked to convert the cutoff frequency on the 0 to PI scale?

Does that sound correct to you?

Thanks in advance.
 
  • #22
andrey21 said:
Hi berkeman I think the answer you are trying to help me find isn't the correct one, having re read the question and the information provided.

Basically I have:

A period of 11 years

A Nyquist frequency of 1/2 month (as sampling interval is one month, using 1/2(delta t)
I am asked to convert the cutoff frequency on the 0 to PI scale?

Does that sound correct to you?

Thanks in advance.

No, not sounding right. First, "frequency" is not plotted on any "0 to PI scale" that I'm familiar with. Phase angle can be plotted on such a scale, but I don't know what you mean by plotting frequency on a phase scale.

And when you make a lowpass filter to help avoid aliasing (or whatever), you want to pass the frequencies of interest, and block frequencies at the sampling frequency and above. The Nyquist frequency is twice the highest signal content frequency, so in this case it would be twice 1/T, or twice 1/11 years. They just happen to be oversampling in this problem, sampling at 12 * 11 the signal period.
 
  • #23
Ok well a more general question then, if a period is 11 years then the frequency is the reciprocal which is 1/11 years, correct?
 
  • #24
berkeman said:
1/(11 years) = 1/(how many seconds?) = ?? * 10^-?? Hz

andrey21 said:
Ok well a more general question then, if a period is 11 years then the frequency is the reciprocal which is 1/11 years, correct?

Correct. Usually frequency is expressed in Hz.
 
  • #25
Ok well I am supposed to use this along with the period and the nyquist frequency to establish a cutoff frequency like I mentioned above into dimensionless scales on the 0 to Pi scale.
 

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