Hi. I am a neuroscientist and I record the firing activity of cells. I am doing some calculations using a program and I realised that I do not know some basics e.g. calculation of frequency and instantaneous frequency. I have not done any maths lectures in a very long time so my knowledge is very basic!

If I start at the basics... If I have two events to work out the frequency I understand it that you take the time between the two events and then do 1/period? If that is correct is that then giving me the instantaneous frequency? I am also interested in average frequency per second. I assume that is taking all of the individual instantaneous frequency values and averaging them by the number of events that happen in a second?

Any help understanding this would be greatly appreciated! Thanks!

 

Frequency is number of events per time, so when you say "average frequency per second," you are saying "number of events per time per time," which I'm pretty sure is not a real measure of anything. Also(and I may be wrong) when you say "instantaneous frequency" I'm pretty sure that such a thing cannot exist; as I said, frequency is number of events per time, and it depends on your sample size/time. Like miles per hour. If you looked down at your car's digital speedometer and said "in this instant I am going 65 miles per hour", you may or may not be right. It would be more accurate to say "in the previous X seconds (my car's speed pulse sample time) my average speed has been 65 mph."

 

@KaraP, That's the right idea. You can also calculate the average frequency by counting the number of events occurring over a given time and divide the number of events by the time in seconds. If the number of events is low, taking the average of the periods will give you better resolution.

 

"average frequency per second" is rate of frequency change, for example,
"miles per hour per second" is a measure of acceleration.

"instantaneous frequency" is a proper terminology.
Taking the reciprocal of the time between two consecutive events is the correct determination of instantaneous frequency.

btw, I've always had a gripe about the definition of "coming to a complete stop at a stop sign". As you rightly suggest, the instantaneous velocity is the measure of distance traveled over time. Depending on the unit of time, one can never determine if a vehicle has come to a complete stop. The definition of "coming to a complete stop" has to include a limit such as "shall not exceed 0.001 m/s".

 

Thanks. I am glad I am on the right tracks. I put all of my data into my program and it works all of this out for me but I was having an issue trying to export my instantaneous frequency as it was asking for the output frequency that I wanted... which then messed up my values. Apparently the program does not have a normal way to copy and paste the absolute values of the inst. frequency but I have found a work around

 

DOH! ... And that's why I'm not a mathematician. Haha. Thanks for the correction Mr. Chips. If I had typed it out in units, ex M/S/S, I might have recognized it as M/S^2 and caught my mistake.

 

...
btw, I've always had a gripe about the definition of "coming to a complete stop at a stop sign". As you rightly suggest, the instantaneous velocity is the measure of distance traveled over time.
...

That's how I treat stop signs too. At any instant in time, the vehicle wheels are at a "complete stop". It's a law of physics. No court in the land could stand up to references from multiple physics textbooks and expert witnesses.

 

Somehow I don't think police have any problem with the concept. Maybe they do, but good luck with that.

 

Ok my last question (for now anyway).

When I report my average frequency I report it as X Hz (I work out my frequency per second) can I also use "Hz" when I report my instantaneous frequency i.e. as instantaneous frequency is not per second can I still use Hz or does Hz not mean frequency per second?

 

Frequency is usually used for something that is periodic, i.e. has a relatively constant frequency. When the events are randomly spaced a preferred unit would be events per second, beats per second, scintillations per second, firings per second, beats per minute, etc.

As stated earlier, frequency per second means something else and is rarely ever used.
Frequency alone means events per unit time.

 

Ok great! Thanks so much!

 

"average frequency per second" is rate of frequency change, for example,
"miles per hour per second" is a measure of acceleration.

"instantaneous frequency" is a proper terminology.
Taking the reciprocal of the time between two consecutive events is the correct determination of instantaneous frequency.

btw, I've always had a gripe about the definition of "coming to a complete stop at a stop sign". As you rightly suggest, the instantaneous velocity is the measure of distance traveled over time. Depending on the unit of time, one can never determine if a vehicle has come to a complete stop. The definition of "coming to a complete stop" has to include a limit such as "shall not exceed 0.001 m/s".

I think if your brakes have transitioned from dynamic to static friction and your tires have transitioned from rolling/skidding to static friction that you have qualified as coming to a complete stop.

 

Ok my last question (for now anyway).

When I report my average frequency I report it as X Hz (I work out my frequency per second) can I also use "Hz" when I report my instantaneous frequency i.e. as instantaneous frequency is not per second can I still use Hz or does Hz not mean frequency per second?

As already pointed out, using the term "frequency per second" does not mean what you are trying to use it for.

In general, no. The unit of Hz (hertz) is "cycles per second' and I believe that it, to be strict about it, it needs to be sinusoidal in nature since 1 cycle is equal to 2τ radians. But I haven't looked into that in detail.

One thing that hasn't been mentioned, and which may or may not be relevant to what you are doing, is that "instantaneous frequency", for many applications, is defined as the derative of the cyclical angle. So say that you have something that starts out at a low frequency (say a tone used as part of an audio test) and ranps to a high frequency. The votlage as a function of time might be:

\(
V(t) = V\sin(\beta t^2)
\)

The argument of the sin() function is the angle as a function of time. The derivative of this, 2βt, is the instantaneous frequency as a function of time.

As I say, this may or may not have any bearing on what you are trying to do.

 

Hello, Kara.

As I understand your application you are talking about pulses, not oscillations.
Oscillations are symmetric and spend half their time above and half their time below zero or other referenece point. Think of a typical sine wave you see in elementary textbooks.

Frequency is applicable to to oscillations.

The terminology for pulses is slightly different.

Two parameters (at least) are of interested in the world of pulses.

Firstly the pulse length, which is self explanatory ( I hope) . This gives you the 'on' time.

Then there is the pulse repetition rate or pulse repetition frequency (PRR)

Note that the off time is usually not the same as the on time.

So you might have a 1 millisecond length pulse, repeated every 10 milliseconds.

So the on time is 1 millisecond and the off time is 9 milliseconds.

The other parameters that may be of interest are the shape of the pulse, perhaps the amplitude (called pulse height), and the fact that in general pulses are all positive or all negative. that is they start from zero and go say 1 volt + or 1 volt -.

I think this is the situation with nerve impulses. The pulse height is important because of the minimum required to achieve a desired effect.

Does this help?