範例：信號與信號分類

函數 > 信號處理 > 信號與系統 > 範例：信號與信號分類

範例：信號與信號分類

信號是代表物理數量或變數的函數或數據集。信號通常會包含有關物理現象行為的資訊；例如，流經電阻器的電流、水底傳播的聲納聲波或地震。在數學運算時，會以自變數 t (通常表示時間) 的函數來表示信號。因此會以 x(t) 表示信號。

連續時間與離散時間信號

若 t 是連續變數，則信號 x(t) 是連續時間信號。若 t 是離散變數 (亦即 x(t) 是在離散時間上定義)，則 x(t) 是離散時間信號，通常表示為 x(n)，其中 n 是整數。離散時間信號 x(n) 可能表示自變數本來就是離散的現象，例如股票每日收盤價格；或可能透過在 t = nT 上取樣連續時間信號 x(t) 取得，其中 T 是取樣時段。

下列範例主要是處理離散時間信號。以下是一些發生頻繁的離散時間信號之範例。

單位階梯信號

1. 使用 Heaviside 階梯函數定義單位階梯函數。

Heaviside 階梯函數指出 f(0)=0.5

2. 定義值域並繪製單位階梯函數。

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單位脈衝信號

1. 定義單位脈衝函數。

2. 繪製單位脈衝函數。

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3. 設定 k 值以將脈衝右移 k 個樣本。

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正弦曲線信號

1. 設定頻率。

2. 定義正弦曲線函數。

3. 繪製正弦曲線函數。

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指數信號

1. 設定 alpha 係數。

2. 定義指數函數。

3. 繪製正弦曲線函數。

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以指數方式衰減的正弦曲線

繪製從正弦曲線函數與指數函數乘積所得出的函數。

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結果為以指數方式衰減的正弦曲線函數。

類比與數位信號

若連續時間信號 x(t) 可採用連續時間間隔內的任意值，則 x(t) 會稱為類比信號。若離散時間信號 x(n) 僅可採用有限數目的相異值，則稱為數位信號。若要將類比信號轉換為數位信號，則需取樣類比信號並加以量化。

實數與複數信號

信號 x(t) 的值若為實數，則為實數信號。同理，信號 x(t) 的值若為複數，則為複數信號。使用函數 phase 與 phasecor 處理複數信號。

定型與隨機信號

定型信號是指在任何指定時間內，會指定其全部值的信號。因此，定型信號可由已知時間函數 x(t) 形成模型。另一方面，隨機信號是指在任何指定時間內，可採用隨機值的信號。隨機信號僅可以統計方式描繪特性。雜訊產生器函數 whiten、gaussn 與 onefn 的設計，是為了產生以使用者定義的統計參數進行特性化的虛擬隨機信號。

相關主題

量子化信號

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