analogaudio
I am trying to self-study this problem for a future exam. The writings in red are solutions to the question. I have a problem in number part e of the question where they find the corresponding level of the samples from the audio signal's equation.
We have 256 discrete levels, and five samples.
I did not understand in part e why does the value of the sample 3V corresponds to the 255th level. and why -1.248 corresponds to the 74th level, and so on…
Any help?
After you've added more info to your question, it would seem that the cause is less to do with the sampling (bit) depth and more to do with the analog connection between two systems.
It looks like you are reaching the limits of the PC's audio output. PCs use line level output, which ranges from +1V to -1Volt. That lines up with the level you are seeing on the myRUI 1900 - you've got a chart there showing the signal in ranging from 1V to -1V which is to be expected.
The signal is clipped because your signal is being clipped by the PC. If you try to send a signal out of the PC with an amplitude that is too high, it will be clipped.
It might be clipping in software before it hits the hardware, or it might be clipping in the hardware. Some parts of the volume controls are in the hardware, some parts are in the software.
The parts of the volume controlling in software can amplify a signal to the point that it can't be represented in 16Bits anymore and gets clipped.
The parts of the volume control in hardware can amplify the signal to the point that the output amplifier itself clips.
In summary:
There are three ways of doing this.
ATMega8 FFT + LCD (Less powerful than Arduino Uno's ATMega328): https://www.youtube.com/watch?v=drhF_F2Xehg
Best Answer
I see, the 2nd sample of the cosine wave is -1.248 volts and this would be between the 74th and 75th quantize levels (effectively 74.752). With ADCs you usually round-down to the nearest integer. This makes it the 74th level.
This is based on dividing the full 6 volt range by 256 to get a quantize step size of 23.4375 mV. Take -1.248, add 3 volts to it to get the range of voltage above -3 volts (binary 00000000). The 2nd sample is therefore 1.752 volts above -3 volts. Then divide 1.752 volts by 23.4375 mV to get 74.752 (quantize step number as a non-integer) - then round down to get the 74th sample.