Q:

How to know Arduino Sampling Rate

/*
fft_adc_serial.pde
guest openmusiclabs.com 7.7.14
example sketch for testing the fft library.
it takes in data on ADC0 (Analog0) and processes them
with the fft. the data is sent out over the serial
port at 115.2kb.
*/

#define LOG_OUT 1 // use the log output function
#define FFT_N 256 // set to 256 point fft

#include <FFT.h> // include the library

unsigned long time;

void setup() {
  Serial.begin(115200); // use the serial port
  TIMSK0 = 0; // turn off timer0 for lower jitter
  ADCSRA = 0xe5; // set the adc to free running mode
  ADMUX = 0x40; // use adc0
  DIDR0 = 0x01; // turn off the digital input for adc0
}

void loop() {
  while(1) { // reduces jitter
    cli();  // UDRE interrupt slows this way down on arduino1.0
    for (int i = 0 ; i < 512 ; i += 2) { // save 256 samples
      while(!(ADCSRA & 0x10)); // wait for adc to be ready
      ADCSRA = 0xf5; // restart adc
      byte m = ADCL; // fetch adc data
      byte j = ADCH;
      int k = (j << 8) | m; // form into an int
      k -= 0x0200; // form into a signed int
      k <<= 6; // form into a 16b signed int
      fft_input[i] = k; // put real data into even bins
      Serial.print("input ");
      Serial.print(i);
      Seirla.print(" = ");
      Serial.println(k);
      fft_input[i+1] = 0; // set odd bins to 0
    }
    fft_window(); // window the data for better frequency response
    fft_reorder(); // reorder the data before doing the fft
    fft_run(); // process the data in the fft
    fft_mag_log(); // take the output of the fft
    sei();
    Serial.println("start");
    for (byte i = 0 ; i < FFT_N/2 ; i++) { 
      Serial.print("\t output");
      Serial.print(i);
      Serial.println(fft_log_out[i]); // send out the data
    }
  }
}

Im using this FFT example code for FFT
cli();  // UDRE interrupt slows this way down on arduino1.0
        for (int i = 0 ; i < 512 ; i += 2) { // save 256 samples
          while(!(ADCSRA & 0x10)); // wait for adc to be ready
          ADCSRA = 0xf5; // restart adc
          byte m = ADCL; // fetch adc data
          byte j = ADCH;
          int k = (j << 8) | m; // form into an int
          k -= 0x0200; // form into a signed int
          k <<= 6; // form into a 16b signed int
          fft_input[i] = k; // put real data into even bins
          Serial.print("input ");
          Serial.print(i);
          Seirla.print(" = ");
          Serial.println(k);
          fft_input[i+1] = 0; // set odd bins to 0
        }

in this input part How much input time period?
Theres no delay(); function in this example
 while(!(ADCSRA & 0x10)); // wait for adc to be ready

this line work like delay() function? and this function how long wait for Analog0?

A:

The sample rate is set in wiring.c: 
https://code.google.com/p/arduino/source/browse/trunk/hardware/cores/arduino/wiring.c?r=565#210
So on an 16mHz arduino has a maximum sample rate of at 9600hz, but the real sample rate highly depends on on the delay you have between conversions.
As your baud rate is pretty high and you don't do a lot of calculation it should somehow be next to 9600hz.
update:
there's a more accurate answer here: https://arduino.stackexchange.com/a/701

