Question

Производится одноканальная (моно) звукозапись с частотой дискретизации 64Гц. При записи использовались 32 уровня дискретизации. Запись длится 4 минуты 16 секунд, её результаты записываются в файл, причём каждый сигнал кодируется минимально возможным и одинаковым количеством битов. Какое из приведённых ниже чисел наиболее близко к размеру полученного файла, выраженному в килобайтах? 1) 10 2) 64 3) 80 4) 512

Answer 1

Формула нахождения объема закодированного звука
A = D * i * t * c (D - частота дискретизации, i - глубина бит/разрядность, t - время, c - кол-во каналов)
Приводим единицы измерения
D = 0.064 кГц = 64.0 Гц
t = 256 c

A = D * i * t * c = 64.0 * 32 * 256 * 1 = 524288.0 бит = 64.0 Kбайт = 0.0625 Мбайт

Answer 2

Calculation of File Size for Mono Sound Recording

To calculate the file size of a mono sound recording, we need to consider the sampling rate, the number of quantization levels, and the duration of the recording.

Given information: - Sampling rate: 64 Hz - Number of quantization levels: 32 - Duration of the recording: 4 minutes 16 seconds

To calculate the file size, we need to determine the number of bits used to represent each sample and then multiply it by the total number of samples in the recording.

Calculation of Bits per Sample

The number of quantization levels determines the number of bits required to represent each sample. In this case, there are 32 quantization levels, which means we need 5 bits to represent each sample (2^5 = 32).

Calculation of Total Number of Samples

To calculate the total number of samples, we need to multiply the sampling rate by the duration of the recording. Since the duration is given in minutes and seconds, we need to convert it to seconds before performing the calculation.

- Duration: 4 minutes 16 seconds - Conversion to seconds: 4 minutes * 60 seconds/minute + 16 seconds = 256 seconds

Now, we can calculate the total number of samples by multiplying the sampling rate (64 Hz) by the duration in seconds (256 seconds):

Total number of samples = 64 Hz * 256 seconds = 16384 samples

Calculation of File Size

To calculate the file size, we multiply the total number of samples by the number of bits per sample and then convert the result to kilobytes.

File size = (Total number of samples) * (Number of bits per sample) / 8 bits/byte / 1024 bytes/kilobyte

File size = (16384 samples) * (5 bits/sample) / 8 bits/byte / 1024 bytes/kilobyte

File size ≈ 10 kilobytes

Therefore, the closest number to the size of the resulting file, expressed in kilobytes, is 10.