I use the following sketch to test if the doorbell speaker reacts on the signal I found. It turned out that it works better when I adjusted the timings a little bit. That's why you won't find 520 microseconds, but 417 microseconds in line 29 of the code.

/* DoorbellSender.ino - Sends signal to Grundig wireless doorbell (model QH-831A)
   when push button is pressed.

   Creative Commons Attribution-ShareAlike 3.0 license
   Original: June 2012 @ Rayshobby.net
   Modified: July 2013 @ crutzen.eu

   Connect data pin of RF sender to digital pin 3 of the Arduino.
   Connect push button to digital pin 2 of the Arduino.

  The signal exists of 24 bits.
  1 means: long  ON followed by short OFF
  0 means: short ON followed by long  OFF
   __                       _____________      _____              __
     |                     |            |     |     |            |
     |_____________________|            |_____|     |____________|

     |     15846us         |    1251    | 417 | 417 |    1251    |
     |                     |            |     |     |            |
     |<--------Sync------->|<--------1------->|<--------0------->|

   To detect the delay values for your device, read the instructions at http://blog.crutzen.eu

*/

#define BUTTON_PIN  2
#define RF_DATA_PIN 3

#define SHORT_DELAY 417
#define LONG_DELAY  (3*SHORT_DELAY)
#define TOTAL_DELAY (SHORT_DELAY + LONG_DELAY)
#define SYNC_DELAY  (38*SHORT_DELAY)

void chime() {

  unsigned long signal = 0b010111110110001000001000;

  for (unsigned char i=0; i<30; i++) { // repeat signal 30 times
    for (unsigned char k=0; k<24; k++) {
      unsigned long d = ((bitRead(signal, 23-k)) == 1 ? LONG_DELAY : SHORT_DELAY);
      digitalWrite(RF_DATA_PIN, HIGH);
      delayMicroseconds(d);
      digitalWrite(RF_DATA_PIN, LOW);    
      delayMicroseconds(TOTAL_DELAY - d);
    }
    delayMicroseconds(SYNC_DELAY);
  }

}

void setup() {                
  pinMode(RF_DATA_PIN, OUTPUT);
  pinMode(BUTTON_PIN, INPUT);
  //chime();
}

void loop() {
  if (digitalRead(BUTTON_PIN) == LOW) {
    chime();
    delay(1000);
  }
}

Source:

• rayshobby.net: Interface with Remote Power Sockets