Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [cosine]

48 questions
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3 answers

Replacing "e" in Euler's formula with another number

Does Euler's formula remain valid if we use any real number other than the constant $e$? For example replacing $e$ with 5 would make the formula look like this: $5^{it}$. I tried this idea in Matlab and replaced $e$ with few other real numbers…
curious
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1 answer

Optimal amplitude of an $m$-bit sinusoid

A continuous-time sinusoid of zero-to-peak real amplitude $A \le 2^{m-1}-0.5$ (e.g., for $m=16$, $A \le 32767.5$) is quantized to $m$-bit resolution by rounding it to the nearest integer (Fig. 1). What is the optimal amplitude for different $m \le…
Olli Niemitalo
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2 answers

Running Integral of sine and cosine functions

In typical signal processing course we were taught that the integral of signal $x(t)$ is given by $$y(t) = \int_{-\infty}^{t}x(\tau) d\tau$$ How can we use this definition to evaluate the integrals of eternal sinusoids, $x(t) = \sin (t)$ or $x(t)…
user5045
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1 answer

Bridging CTFT and DTFT for a cosine

I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT. For example if I take a basic example: $$\begin{aligned} x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \cdot \left( e^{j\omega_x t} + e^{-j\omega_x t} \right)…
Yannick
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3
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2 answers

DTFT of sine wave using freqz

As mentioned in the title, is it possible to use freqz to find the DTFT of a sine wave? I am confused about what the 'a' and 'b' vectors would look like, since there are only impulses in the numerator.
Pranav Krishnan
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1 answer

What are the cosine functions in JPEG's DCT-II table?

As I understand it from this video, in a JPEG image an 8x8-pixel block is made up of weighted cosine waves, calculated using DCT-II. There are lots of visualizations of these waves, such as this one from the Wikipedia article on JPEG…
JeffThompson
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1 answer

Sinusoid with increasing frequency

How would you describe this signal? It's like a sinusoid but as if its frequency was constantly increasing: could you write down a mathematical description? Thanks. And no, this is not homework...
MisterH
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A question about sampling rate of cosine signal

Given $$c(t) = \cos(2\pi\cdot 30 \cdot t) $$ If we sample this signal at the Nyquist rate 60 Hz and at a higher rate of 80 Hz, we get the following: There is no aliasing as $f$ = 30 Hz is less than or equal to the folding frequency, 30 Hz and 40…
Morcus
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How would one design a (quasi) linear phase adaptive notch filter for a single complex tone?

While IIR notch filters are attractive, I need to retain phase linearity at the filter output. I imagine that it's possible to use a standard IIR notch …
rhz
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Why MATLAB fft cos makes imaginary parts?

The cos fourier transform has no imaginary parts, but in this code it has imaginary parts that little…
Park
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1 answer

Linear prediction (LPC) of Sine wave samples around maximas

I think I missed class when this was explained ... Anyway as part of a bigger project I have to implement a LPC to predict 2-3 future values of a sinusoidal process. I wrote a small Matlab m-file to calculate the predictor coefficients and plot the…
Skaveelicious
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Integration of Sinusoidal functions

Since Differentiation of a sinusoidal function of a certain angular frequency gives a sinusoidal function of the same frequency, does the statement "Integration of a sinusoidal function of certain frequency gives again a sinusoidal of same…
Mathpdegeek497
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Z-transform of $\cos(\omega_0 n(n+1))u[n]$

I'm doing some research on Zadoff-Chu sequences and as a part of it I wanted to find the Z-transform of: $$\cos(\omega_0 n(n+1))u[n]$$ Wolfram Alpha / Mathematica couldn't help out. I couldn't find a way to do this from identities so I tried doing…
Eduards
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Setting up RRC filter and useful equations

I have looked at previous answers but cant seem to get everything I need in one place to help me and my textbook doesnt explain this in practical terms. Signal Parameters: $F_s = 44100$ $R_s = 300$ $sps = F_s / R_s$ Now my Raised Cosine filter…
Natalie Johnson
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Optimization of harmonics calculation

I need to compute the sine and cosine of an argument along with n "harmonics" \begin{matrix} \sin(x) & \cos(x) \\ \sin(2x) & \cos(2x) \\ \cdots \\ \sin(nx) & \cos(nx) \end{matrix} This takes a lot of computing time and since this is a real-time…
Ben
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