i need a help
i know that the differentiation of a square wave creates a spike wave
but what if the input wave is the spike wave ? how would its differentiation look like ?
can u please help

 

hi GB,
As you are interested in signal pulses, look thru these two PDF's
E

 

 

is there a way to turn it into a sine wave ?

 

You can analyze a differentiator from the perspective of frequency domain.
A differentiator is also a high pass filter. It attenuates low frequencies while it passes high frequencies.

Two differentiators cascaded alters the frequency response of the high pass filter.

In order to turn the square wave into a sine wave, you need a narrow band pass filter or a tuned resonator.

 

is there a way to turn it into a sine wave ?

Yes. Synchronize sine generator with spike series.

 

https://en.wikipedia.org/wiki/Heaviside_step_function → https://en.wikipedia.org/wiki/Dirac_delta_function → https://en.wikipedia.org/wiki/Unit_doublet → https://www.quora.com/What-are-unit-step-unit-ramp-unit-impulse-unit-doublet-and-parabolic-functions

 

You can double integrate a square wave to get a sinewave.

 

You can double integrate a square wave to get a sinewave.

But that's not a true sine wave is it?

 

You can double integrate a square wave to get a sinewave.

I don't believe that's correct; it's equivalent to saying that you can double differentiate a sine wave to get a square wave, which is obviously untrue since no matter how many times you differentiate a sine wave you simply end up with another sinusoid.

Double integrating a square wave will certainly reduce the amplitude of the fundamental's harmonics drastically and yield a much "rounded" waveform; but it will not be a sine wave since the harmonics are not reduced to zero.

 

i need a help
i know that the differentiation of a square wave creates a spike wave View attachment 185144
but what if the input wave is the spike wave ? how would its differentiation look like ?
can u please help

Look up "unit doublet"

If you differentiate a pulse you get two impulses one positive and one negative. If you let the pulse width tend to zero you get a doublet. Conceptually it's like a positive impulse with an immediate negative impulse.

With concepts like this is it more important to understand the effects it has on other things like circuits especially filter circuits than what it really means all by itself.

 

I don't believe that's correct; it's equivalent to saying that you can double differentiate a sine wave to get a square wave, which is obviously untrue since no matter how many times you differentiate a sine wave you simply end up with another sinusoid.

Double integrating a square wave will certainly reduce the amplitude of the fundamental's harmonics drastically and yield a much "rounded" waveform; but it will not be a sine wave since the harmonics are not reduced to zero.

Yeah i agree we should not say that double integration of a square wave produces a sine wave unless we add a qualifier such as that the sine wave is not a perfect sine wave.
It's really two exponentials and can easily be shown to just *approximate* a sine wave.

 

It's really two exponentials and can easily be shown to just *approximate* a sine wave.

I believe that double integration of a square wave yields a sequence of parabolas of alternating polarity, not a sequence of exponentials. Integrating a constant yields a ramp, and integrating a ramp yields a parabola.

 

I believe that double integration of a square wave yields a sequence of parabolas of alternating polarity, not a sequence of exponentials. Integrating a constant yields a ramp, and integrating a ramp yields a parabola.

Yes i called it exponential but meant its a second degree expression. Ive plotted the two on top of each other and the difference is clear. ill plot again.

 

It's really two exponentials and can easily be shown to just *approximate* a sine wave.

True, I should have stated that.
The Ltspice simulation below gives a total harmonic distortion of 3.7% for the double-integrated square-wave, which may be good enough for some applications.

 

True, I should have stated that.
The Ltspice simulation below gives a total harmonic distortion of 3.7% for the double-integrated square-wave, which may be good enough for some applications.

View attachment 185165 View attachment 185166

Hi,

Yeah for most i would bet except fine audio tests.
Back in the 1980's i used a nonlinear sine generator which used nonlinear wave shaping starting with a triangle and i would have loved to have a wave as good as 4 percent THD (ha ha).

 

i know that the differentiation of a square wave creates a spike wave
but what if the input wave is the spike wave ? how would its differentiation look like ?

A "spike wave" has a very fast leading edge just like a square wave, and that is what "gets through" a differentiator. The output will be another spike, and its shape will depend on the relationship between the width of the input spike and the time constant of the differentiator. The longer the time constant, the more the output spike will be exactly like the input spike. As the time constant gets shorter, the output spike gets narrower than the input, and with lower peak amplitude.

ak

 

Here is my simulation using a behavioral source to generate the polynomial of interest...

The calculated THD using 1001 harmonics came out to 3.80405 percent and agrees with LTSpice with 1001 harmonics.

The calculated harmonics are found from the Bn which simplifies into:
B[n]=(8*pi*n*sin(pi*n)+16*cos(pi*n)-16)/(pi^3*n^3)

and that is divided by the first harmonic B[1], squared, then summed from 2 to N
then the square root is taken to get the fractional THD, then multiply by 100 to get the THD in percent.

Here is the 21 digit THD in percent with 100001 harmonics:
3.80404605774183799705

and that should be accurate to that many digits.
Just to note, with 41 harmonics the THD in percent rounds to 3.80405 as in LTSpice.

 

thanks for ur help everyone but i'm actually stuk with this circuit
what i can't understand is how did waveform E turn into waveform F ? how could a spike wave like E turn into a sine wave like F ?

 

i need a help
i know that the differentiation of a square wave creates a spike wave View attachment 185144
but what if the input wave is the spike wave ? how would its differentiation look like ?
can u please help

The spike has infinite slope. So if you differentiate IT the result is also a spike of infinite slope. There's little difference in those kinds of infinities. But in practice it's not really a spike