> ## Documentation Index
> Fetch the complete documentation index at: https://prod-mint.classiq.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Discrete Sine Cosine Transform

Functions:

| Name            | Description                       |
| --------------- | --------------------------------- |
| `qct_qst_type1` | \[Qmod Classiq-library function]. |
| `qct_qst_type2` | \[Qmod Classiq-library function]. |
| `qct_type2`     | \[Qmod Classiq-library function]. |
| `qst_type2`     | \[Qmod Classiq-library function]. |

### qct\_qst\_type1

<pre><code>qct\_qst\_type1(
x: QArray\[QBit]
) -> None</code></pre>

\[Qmod Classiq-library function]

Applies the quantum discrete cosine (DCT) and sine (DST)
transform of type 1 to the qubit array `x`.
Corresponds to the matrix (with $n\equiv$`x.len`):

$$
\left(
egin{array}{ccc|c}
{} &{} &{} \
  {}&{
m DCT}^{(1)}(2^{n-1}+1) & {}& 0\
  {} &{} &{} \
  \hline
  {} & 0 & {} & i{
m DST}^{(1)}(2^{n-1}-1)
\end{array}

ight)
$$

**Parameters:**

| Name | Type           | Description                                | Default    |
| ---- | -------------- | ------------------------------------------ | ---------- |
| `x`  | `QArray[QBit]` | The qubit array to apply the transform to. | *required* |

### qct\_qst\_type2

<pre><code>qct\_qst\_type2(
x: QArray\[QBit],
q: Const\[QBit]
) -> None</code></pre>

\[Qmod Classiq-library function]

Applies the quantum discrete cosine (DCT) and sine (DST)
transform of type 2 to the qubit array `x` concatenated with `q`, with `q` being the MSB.
Corresponds to the matrix (with $n\equiv$`x.len`+1):

$$
\left(
egin{array}{c|c}
  {
m DCT}^{(2)}(2^{n-1}) & 0\
  \hline
  0 & -{
m DST}^{(2)}(2^{n-1})
\end{array}

ight)
$$

**Parameters:**

| Name | Type           | Description                                                | Default    |
| ---- | -------------- | ---------------------------------------------------------- | ---------- |
| `x`  | `QArray[QBit]` | The LSB part of the qubit array to apply the transform to. | *required* |
| `q`  | `Const[QBit]`  | The MSB of the qubit array to apply the transform to.      | *required* |

### qct\_type2

<pre><code>qct\_type2(
x: QArray\[QBit]
) -> None</code></pre>

\[Qmod Classiq-library function]

Applies the quantum discrete cosine (DCT)
transform of type 2, $\{
m DCT\}^\{(2)\}$, to the qubit array `x`.

**Parameters:**

| Name | Type           | Description                                | Default    |
| ---- | -------------- | ------------------------------------------ | ---------- |
| `x`  | `QArray[QBit]` | The qubit array to apply the transform to. | *required* |

### qst\_type2

<pre><code>qst\_type2(
x: QArray\[QBit]
) -> None</code></pre>

\[Qmod Classiq-library function]

Applies the quantum discrete sine (DST)
transform of type 2, $\{
m DST\}^\{(2)\}$, to the qubit array `x`.

**Parameters:**

| Name | Type           | Description                                | Default    |
| ---- | -------------- | ------------------------------------------ | ---------- |
| `x`  | `QArray[QBit]` | The qubit array to apply the transform to. | *required* |