# Suggest some continuous signal

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I'm reading a book on DSP, and they say that there are discrete and continuous kinds of signals. I can imagine some discrete signals, but i have no idea of what could a continuous signal be. Can you suggest some?

An audio file?

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An audio file?

wouldn't that be a discrete signal as it can only be 2^16 different levels (assuming a bit depth of 16)

continuous signal would be more what you get from a microphone or antenna, an analogue signal.

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I was thinking more on the processed output side, but yeah. I just didn't get the question and it was sitting there.

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There are lots, room temperature, mains voltage...

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Oh, analogue signals are the continuous signals. I couldn't think about them because i thougt they had a limit due to natural properties.

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Yes, continuous == analogue and discrete == digital. Sometimes discrete signals can be embedded in continuous signals ie. surround sound signals for home theater.

Technically, as in the example of the audio file, a Digital Analogue Converter could be called a Digital Signal Processor. The analogue waveform, on hard disk, is a digital representation with bit depth and sample rate, and so on. A DAC will take this discrete signal and convert it to a continuous or analogue signal.

I'm curious what natural constraints you were envisioning onto analogue signals as so they were not contiguous with continuous signals?

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Continuous signals are signals in which their time steps and magnitude steps are infinitely small (ie, ~zero).

Discrete signals are signals in which their time steps and/or magnitude steps are measurable (ie, non-zero). Any digital file must be a discrete signal because it consists of quantitized values from various periods in time. A vinyl record is an example of a continuous signal.

Signal samples are discrete in nature. If you google "continuous signal" "discrete signal", you'll find a pdf from the University of Rochester that has a diagram on page 4 of a continuous signal and its discrete sampled signal that shows how the discrete signal misrepresents the original continuous signal because the sampling rate is too slow.

As for limitations of analog signals, circuitry can "clip" (ie, limit) a signal, but this clipping only reduces the signal's fidelity (to the original signal) but not it's "continuous" nature.

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I wasn't envisioning something specific, i just thought that the natural structure of one object may allow only a finite level of variation on it's properties.

I'm also not very sure if i understand what discrete and continuous means, i had a naive definition that, for example, a continuous signal would be a signal that could vary between $-\infty$ to $\infty$.

But i've read that when the continuous signal is captured and transformed into discrete signal, it's quantized. This made me think: On a quantized signal, you'll have intervals like 0 - 1, and if you capture say: 0.6 it's gonna be transformed in 1. Now i'm thinking that the continuous signal is the signal that, by not having a quantization, allow $\frac{y}{x}$ with $x$ being any number. On a discrete signal, $\frac{y}{x}$ will be rounded to the nearest interval, instead of being recorded as it is.

Continuous signals are signals in which their time steps and magnitude steps are infinitely small (ie, ~zero).

Discrete signals are signals in which their time steps and/or magnitude steps are measurable (ie, non-zero). Any digital file must be a discrete signal because it consists of quantitized values from various periods in time. A vinyl record is an example of a continuous signal.

Signal samples are discrete in nature. If you google "continuous signal" "discrete signal", you'll find a pdf from the University of Rochester that has a diagram on page 4 of a continuous signal and its discrete sampled signal that shows how the discrete signal misrepresents the original continuous signal because the sampling rate is too slow.

As for limitations of analog signals, circuitry can "clip" (ie, limit) a signal, but this clipping only reduces the signal's fidelity (to the original signal) but not it's "continuous" nature.

I was deducting it just now. But thanks for the answer.

Edited by BeuysVonTelekraft
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Given the example of an audio wave file, bit depth and sample rate.

We can represent the amplitude of a continuous wave using the bit depth. If we have a bit depth of 16bits then the amplitude of the analogue wave can be represented by 2^16 values.

We can then sample the amplitude by a given sample rate. So if the sample rate is 44kHz we sample the amplitude of a wave 44000 times per second.

There is a good deal of rounding going on in this process and converting a continuous wave to a discrete representation tends to be pretty lossy. The application however, determines the detail of the representation used.

I don't know if this helps any but . . . .

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Given the example of an audio wave file, bit depth and sample rate.

We can represent the amplitude of a continuous wave using the bit depth. If we have a bit depth of 16bits then the amplitude of the analogue wave can be represented by 2^16 values.

We can then sample the amplitude by a given sample rate. So if the sample rate is 44kHz we sample the amplitude of a wave 44000 times per second.

There is a good deal of rounding going on in this process and converting a continuous wave to a discrete representation tends to be pretty lossy. The application however, determines the detail of the representation used.

I don't know if this helps any but . . . .

Yeah, yeah. I got it. I knew this process of audio conversion, i just didn't know this difference of continuous and discrete. Now it's perfectly clear to me, unless there are some other ill implications on the terms.

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You have to study both Discrete and Continuous Signal Processing .. because waves in reality are continuous, but you cannot model them on the computer as a continuous, you have a bit-rate on which you model that continuous signal as a discrete signal on the computer, continuous (real) signal have many properties that are modeled through BLUE matrix,

Continuous means it covers all points through an interval, Discrete means we have a value on some (discrete) points

One example as mentioned, is a sound file .. the sound is stored on the hard disk as a discrete signal with its properties, when played .. a complex analysis-based transformation rebuild a continuous signal that is not the exact as the original, but close enough

Edited by khaled
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Yup, i understand it now, i even did a notebook on Mathematica for the case I need to explain it to someone in the future.

The first image is a - theoretically - continuous signal, the second is the discrete signal and the y slider is the quantization level.

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Let's make a simple example .. Consider the temperature of your city during the day, it continuously changing .. it's impossible to gain the continuous interval of it

But you simply, for example, take the value of the temperature every hour for example, this means you have 24 samples per day

you also keep other properties of the temperature, which will help you re-build the temperature change during that day, like, for example, the average mid-point between the discrete points, ..etc

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