9

This depends a lot on how you implement it. A single biquad takes about 10 arithmetic operations. (To be precise a Transposed Form II takes 4-5 multiplies and 3 adds, depending on how the gain management is done). Arithmetic operation translates into clock cycles of your processor. That depends a lot on the efficiency of your instruction set and how good yo ...


6

Note that the inverse of an FIR system is IIR, and the same is true for the inverse of an IIR system, unless it is an all-pole system, the inverse of which would be FIR. So in most cases the ideal equalizer should have an infinitely long impulse response in order to perfectly invert the channel. In practice almost all adaptive equalizers are FIR filters ...


5

Assuming that you also want to equalize the filter's phase response (not only its magnitude response), you need an equalizer with a transfer function $E(z)$ that is the inverse of the FIR filter's transfer function $H(z)$: $$E(z)=\frac{1}{H(z)}=\frac{1}{c_0+c_1z^{-1}+\ldots+c_{N-1}z^{-(N-1)}}\tag{1}$$ This is an all-pole filter which can be implemented by ...


5

I don’t think you’re alone, but essentially this is simply a problem of optimization. Let’s say you have a processor with a 88MHz clock. That’s 2k clocks per sample at 44kHz. If we take the term ‘most’ to mean 50%, of the clocks, then that leaves 1k clocks per sample for filtering. Running 8 filters leaves 125 clocks per filter. That’s a decent amount of ...


4

Ok, there is some misconceptions in your question. I strongly recommend you to read a little more about the topics, but I will try to help you a little. My answers and some comments: ...linear equalizer is a filter that can undo these channel effects. When the channel coefficients w are unknown, we perform blind equalization. In this scenario, we ...


3

A filter bank system is generally composed of: an analysis filter bank, that split an input signal into components with filters and may reduce their rate a synthesis filter bank (FB), that takes the components, potentially increase their rate, and feed them into filter elements so that the novel outputs can be combined into a signal. It is perfect ...


3

it looks like this eq10q uses cascaded parametric EQs, initially set up to be bell, but switchable to other types (like shelving). i wouldn't doubt that they're using the audio EQ cookbook. if you're using that, there is a parameter called "shelf slope" or $S$ that is often set to 1, because that gets you the steepest slope without dips or lips or bumps. ...


3

Thanks for the answer. You are correct - the training sequence is known by the time you establish any communication. In case if somebody stumbles upon this in the future, here's how to get this done: The synchronization burst contains an extended training sequence. It's longer than the regular one and there is only one sequence. You are supposed to use ...


3

I checked your code in my PC, you need just to delete the delay added before the filter. For example, you can use: U_aft_fil = U_aft_fil(fil_delay+1:end); Then when filtering it again at the receiving side, you delete it again : U_r_fil = U_r_fil(fil_delay+1:end); Good luck


3

Don't worry too much about defining these terms too precisely, because they are used in many contexts with slightly different meanings. In very general terms, "estimation" is the calculation of a signal parameter, for example the phase, the mean, the PSD, etc. In other words, you have a signal, possibly noisy or distorted, and you want to find ...


3

As far as equalizer performance and possible limitations I provide two key points below about the span of the equalizer and the number of samples per symbol to use. The equalizer duration in time is set to match the time duration of the delay spread of the channel (since this is the distortion the equalizer will compensate for). If it is much less than there ...


2

result[i] = band_gain[0] * LPF(t, band_freq[0]) + band_gain[1] * (LPF(t, band_freq[1]) - LPF(a, band_freq[0])) + band_gain[2] * (LPF(t, band_freq[2]) - LPF(a, band_freq[1])) + band_gain[3] * (LPF(t, band_freq[3]) - LPF(a, band_freq[2])) + band_gain[4] * (IMPULSE(t) - LPF(t, band_freq[3])); is actually very simple to explain with pictures. First we assume f0 ...


2

From the referenced description and also from [1] it seems to me that the training sequence (here: midamble) is assumed to be known already. This knowledge has probably been acquired before in the synchronization burst. The first block in Fig. 2 extracts the training sequence from the received signal. This suggests that the receiver is already synchronized ...


2

A typical communications system is composed of the following parts: Message (Information Source) --> Encoding --> Modulation --> Channel --> Demodulation --> Decoding --> Recovered Message A "chaotic modulator" is just another way of doing the Modulation building block. This is depicted in Figure 1 of the paper that is cited in the ...


2

This depends a bit on what you want to get out of this and how much effort/work you are willing to put in. Doing a room EQ that actually works and makes it sound consistently better is quite complicated. There are commercial systems available but they tend to be complicated and expensive or tied to a specific product. A really good freeware option to play ...


2

Does an audio equalizer consist of a perfect-reconstruction filterbank? Short answer: No. It's a bit unsharp what you're asking here, since reconstruction filterbanks are usually things that combine multiple, separate, independent signals back into one signal, but let's assume this makes sense here, and your audio source magically produces one signal stream ...


2

The audible range is about 10 octaves, and usually the center frequencies of a graphic equalizer would be distributed equally spaced on a log scale to cover that range. Common equalizers have either $30$ bands (with $1/3$ octave filters) or $10$ bands (with $1$ octave filters). If you want $5$ bands, you could choose filters that cover approximately $2$ ...


2

Most likely people use different words to describe the same concept. This happens quite often. The TEQ is the more general term and also used to equalize other methods that OFDM, while CS is related to OFDM and tries to make the channel shorter so that it fits within the CP duration. You can check online, you will find that almost all articles related to CS ...


2

If the received signal can be written as $$\mathbf{y} = \mathbf{H}\,\mathbf{x} + \mathbf{n}$$ where $\mathbf{H}$ is the channel matrix, $\mathbf{x}$ is the transmitted vector, and $\mathbf{n}$ is the AWGN of the channel, then a zero forcing equalizer is simply (assuming that the channel matrix is square, and it's estimated perfectly at the receiver) $$\...


2

This could be homework, so I'll only give you a few hints to help you solve the problem yourself. Remember that a ZF equalizer just inverts the channel, so if $D(z)$ is the equalizer's transfer function, what must be the result of the product $C(z)D(z)=?$. From this equation you obtain $D(z)$, which is IIR. Let the coefficients of $D(z)$ be $d[n]$, i.e., $$...


2

Not a comprehensive source of details, but for me this paper/tutorial has been the most helpful in terms of principles explanation. Also here you can find a basic working example of DFE implementation in python, that you may find helpful.


2

The purpose of the loudness filter is to compensate for the level dependency of the a human's "frequency response". Most music is mixed at pretty high levels, say at 80-90 dB SPL. If you play this back at much lower levels, say 40 dB SPL, it will sound very bass deficient. The loudness filter compensates for this by boosting the bass at lower ...


2

This is just a nice way to rewrite Equation (2). Using Block matrix interpretation: \begin{align} \underline{H}^H\underline{H}=\begin{bmatrix}H_{R\times T}^H&\sigma I_T\end{bmatrix}\begin{bmatrix}H_{R\times T}\\\sigma I_T\end{bmatrix}=H_{R\times T}^HH_{R\times T}+\sigma^2I_T \tag{a} \end{align} \begin{align} \underline{H}^H\underline{y}=\begin{bmatrix}H_{...


1

There's no universally acclaimed correct design of equalizers. Just like there are multiple car designs per brand, there are also multiple techniques for achieving desired effects. It's true that your channel filters will interact with each other and change the effective resulting gain at each frequency, but mostly pronounced at the adjacent channel peak ...


1

You need an estimate of the channel to receive the sequence but the zero-forcing equalizer does not need the channel response as an input. The zero forcing equalizer estimates the channel response. This can be done either with a training sequence, or can be decision directed when signal to noise ratios are high enough. Given the received signal is the ...


1

In an initial phase, the training sequence is used to determine the optimal equalizer weights. There is usually no reason to leave the weights fixed because you need an adaptation algorithm to compute the initial weights from the training sequence, so you might as well continue running the adaptation algorithm as soon as actual data are transmitted. If the ...


1

The error should be minimized between the equalized signal and what? There is no known sequence in this case. But there is: if the channel is still good enough so you can decode a packet successfully, you can reconstruct the original signal by simply re-encoding the packet.


1

If the channel just adds noise and does not cause any distortion (as in the first figure), you can design the transmit filter $g(t)$ such that, when combined with its matched filter at the receiver, the Nyquist criterion for zero intersymbol interference (ISI) is satisfied. If the channel adds linear amplitude and phase distortion (as in the second figure), ...


1

With a blind equalization technique like the constant modulus algorithm (which is often implemented using a least mean squares (LMS) filter as you indicated), you aren't directly estimating the channel impulse response itself. Instead, the signal model is like this: The receiver observes the following signal: $$ x[k] = s[k] * c[k] + n[k] $$ where: $s[k]$ ...


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