What does it mean that not every signal starts and ends perfectly in frequency ?

[jani12]

From the book titled "Digital Signal Processing and the Microcontroller"
"Not every signal necessarily starts and ends perfectly in frequency, so we often use the point where the signal has one-half the peak power. (As we'll see later, this corresponds to 1 / sqrt(2), or roughly 0.7 of the largest value in the spectrum when talking about voltage or current.)"

Please explain visually with at least one example.

>> "Not every signal necessarily starts and ends perfectly in frequency"
Does this mean that at the start and end the signal is not a sinusoid ?

>> "roughly 0.7 of the largest value in the spectrum when talking about voltage or current.)"
My understanding is that in spectrum there are many sinusoids of different frequencies. At least some of them won't have 0.7 of the largest value in the spectrum? Does this mean they won't be considered?

 

[KlausST]

Hi,

I guess we need some more context. What is the chapter about?

I can only guess it has to do with the processing of some sine shaped signal. Maybe some digital filter or RMS calculation...

Klaus

 

[crutschow]

Does this mean that at the start and end the signal is not a sinusoid ?

I think it means the signal is still basically sinusoidal, but the frequency may be somewhat different.

My understanding is that in spectrum there are many sinusoids of different frequencies. At least some of them won't have 0.7 of the largest value in the spectrum? Does this mean they won't be considered?

I think that's just to determine where to stop analyzing the signal.
I would expect all the spectrum frequency components to still be considered.

 

[BradtheRad]

0.7 of the largest value in the spectrum

I have a hunch the chapter is translated from another language. Instead of spectrum we could say amplitude. Every sine waveform's peak amplitude is 1.414 times its 'nominal' value. 1.414 equals square root of 2.
Thus to find nominal value given peak amplitude, multiply by .707.

Example, In the US we call house voltage 120 VAC mains. Peaks are 170 volts amplitude positive and negative polarity.

About starting and ending perfectly...
Since the book is about digital signals, it may tell how a sinewave is a sensible carrier for each individual signal when all channels must share radio airwaves (or cables or fiber optics) simultaneously. Consider a raw digital transmission with sudden starts and stops. This generates noise and interference. Therefore the ones and zeroes must be encoded in a sinewave which should start and stop at zero amplitude so that it does not generate interference.

 

[D.A.(Tony)Stewart]

When analyzing power density from a capture in the time domain, we use average power over an integer number of cycles. If the spectrum contains many spectral sine components then it is written to use the dominant frequency at 70% of peak voltage for start and end of the capture to approximate the 50% power threshold.

If analyzing in the voltage domain, then one would use 50% of the average peaks not including over/undershoot, such as for a pulse.

 

[jani12]

This is the background chapter. This is chapter 2 in the book, Analog Signals and Systems. Filtering starts in Chapter 3.

 

[KlausST]

Hi,

I found a MOTOROLA book online with the same title.

But I can not find one of your statements in it.

Klaus

 

[FvM]

The quoted chapter talks about signal bandwidth metric. No assumptions about time domain and waveforms, e.g. sinoid.

 

[KlausST]

The quoted chapter talks about

In the Motorola book?
Did you find those texts like
"Not every signal necessarily starts and ends perfectly in frequency"
or
"roughly 0.7 of the largest value in the spectrum when talking about voltage or current.)"

I did not.

Klaus

 

[margotandrew]

Yeah You are right.

 

[D.A.(Tony)Stewart]

The important thing to realize is that power spectral density or power of any repeating signal requires full cycles. e.g 1 to N repeating cycles, otherwise the spectrum of the step pulse discontinuity gets added to the result.

This is related to why Power is always measured as average = Pd and not RMS power. Single pulse power measurements however are an integrated VI product.

RMS Power is used for effective radiated power where heat rise is not a metric but often misused for audio power amps.

For more clarity https://www.analog.com/en/resources/analog-dialogue/raqs/raq-issue-177.html

When it comes to transistors the peak power is shown higher than average using the Safe Operating Area or SOA plots with duty cycle vs current or switched power vs ambient temperature. These are hard limits to avoid with design margins.